Key takeaways
- Find a vector between two points by subtracting the start coordinates from the end coordinates.
- Magnitude is the square root of the sum of squared components; (3, 4) has length 5 and (2, 3, 6) has length 7.
- Use atan2 for direction in 2D and unit vectors for direction in 3D.
- The dot product gives a number and the angle between vectors; the cross product gives a perpendicular vector.
- Embedding search uses the same math: cosine similarity compares vector directions.
To find a vector between two points, subtract the start point's coordinates from the end point's: from A(1, 2) to B(4, 6), the vector is (3, 4). From there you can find its magnitude, direction and products, the same operations that power embedding search in RAG systems, where cosine similarity compares text vectors. I build retrieval systems such as RAG.NextUpgrad, so this page covers finding vectors, magnitude, 3D length, direction, products, vector quantities, size in code, calculators, line equations and vector images.
How do you find a vector?
Subtract coordinates: the vector from point A to point B is B minus A. For A(1, 2) and B(4, 6), the vector AB is (4 - 1, 6 - 2) = (3, 4). It describes how far and in which direction to move from A to B.
Also asked as: how find vector
In 3D, do the same with three coordinates: from (1, 0, 2) to (3, 4, 5), the vector is (2, 4, 3). You can also find a vector from a magnitude and direction: a speed of 10 at 30 degrees above the x-axis gives (10 cos 30°, 10 sin 30°), about (8.66, 5). In machine learning, vectors are found differently: an embedding model converts text or images into vectors of hundreds of numbers, positioned so similar meanings sit close together.
How do you find vector magnitude?
The magnitude, or length, of a vector is the square root of the sum of its squared components. For v = (3, 4), |v| = sqrt(3² + 4²) = sqrt(25) = 5, which follows from Pythagoras' theorem.
Also asked as: how to find vector magnitude
The same rule works in any number of dimensions: square each component, add them, and take the square root. In Python, numpy.linalg.norm(v) computes it. Magnitude is never negative, and only the zero vector has magnitude zero. Dividing a vector by its magnitude gives a unit vector, of length 1, pointing the same way. Embedding systems often normalise vectors this way, so that the dot product of two vectors equals their cosine similarity, which makes search faster and simpler.
How do you find the length of a 3D vector?
Use |v| = sqrt(x² + y² + z²). For v = (2, 3, 6), the length is sqrt(4 + 9 + 36) = sqrt(49) = 7. It is the straight-line distance from the origin to the point (2, 3, 6).
Also asked as: how to find length of 3d vector
To find the distance between two points in 3D, first subtract them to get the vector between them, then take its length. From (1, 1, 1) to (3, 4, 7), the vector is (2, 3, 6), so the distance is 7. This formula is just Pythagoras applied twice: once in the xy-plane, then again with the z component. Common slips are forgetting that squared negative components become positive, and forgetting the final square root.
How do you find vector direction?
In 2D, the direction is the angle the vector makes with the positive x-axis: θ = atan2(y, x). For (3, 4), θ = atan2(4, 3), about 53.13 degrees.
Also asked as: how to find vector direction
Use atan2 rather than plain arctan of y over x, because atan2 accounts for the quadrant: (-3, -4) points at about -126.87 degrees, or 233.13 degrees, not 53.13. In 3D, direction is usually described by the unit vector, the vector divided by its magnitude, or by direction cosines, the cosines of the angles with each axis. For (2, 3, 6) with length 7, the unit vector is (2/7, 3/7, 6/7). In embedding search, direction is what matters: cosine similarity compares directions and ignores length.
How do you find a vector product?
There are two products. The dot product multiplies matching components and adds them, giving a number: (1, 2, 3) · (4, 5, 6) = 4 + 10 + 18 = 32. The cross product, for 3D vectors, gives a new vector perpendicular to both.
Also asked as: how to find vector product
For a = (a1, a2, a3) and b = (b1, b2, b3), the cross product is (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1). For (1, 2, 3) and (4, 5, 6), it is (2·6 - 3·5, 3·4 - 1·6, 1·5 - 2·4) = (-3, 6, -3). The dot product also gives the angle between vectors: cos θ = a · b / (|a| |b|), which is exactly cosine similarity in RAG retrieval. Use numpy.dot and numpy.cross in Python.
How do you find a vector quantity?
A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, force and momentum. A scalar quantity has only magnitude, such as distance, speed, mass, temperature and time.
Also asked as: how to find vector quantity
To decide whether a quantity is a vector, ask whether direction changes its meaning: 5 metres north differs from 5 metres south, so displacement is a vector, while 5 kilograms has no direction. To find a vector quantity, measure its size and direction, then express it in components, so a force of 10 newtons at 30 degrees becomes about (8.66, 5) newtons. In data science, vector simply means an ordered list of numbers, such as an embedding, even without physical direction.
How do you find vector size?
Size can mean two things: magnitude, the geometric length, or the number of components, also called the dimension. In code, size usually means the number of elements: len(v) in Python, v.shape in NumPy, and v.size() for a C++ std::vector.
Also asked as: how to find vector size
For embeddings, the dimension is fixed by the model, for example 384, 768, 1024 or 1536 numbers per vector, and your vector database index must be created with that exact dimension. A mismatch is a common error when switching embedding models. Larger dimensions can capture more detail but use more memory and slow search, so some models support shortening vectors. To find a vector's magnitude instead, take the square root of the sum of squares, as above.
How do you find a vector in a calculator?
Scientific calculators such as the Casio fx-991 series have a vector mode: enter each vector's components into VctA or VctB, then compute dot products, cross products, magnitudes with Abs, and angles. Menu names vary by model, so check its manual.
Also asked as: how to find vector in calculator
To find a vector between two points by calculator, subtract coordinates manually or store the points as vectors and subtract them. Online tools such as Wolfram Alpha and GeoGebra accept expressions like norm of (3, 4) or the cross product of two vectors and show steps. In Python, NumPy does all of this in one line, which is useful for checking homework or computing many vectors at once, such as similarity scores for thousands of embeddings.
How do you find the vector equation of a line?
A line through point A with direction vector d has the vector equation r = a + t·d, where a is A's position vector and t is any real number. Each value of t gives a point on the line.
Also asked as: how to find vector equation of line
To find it from two points A and B, use d = B - A. For A(1, 2, 3) and B(4, 6, 8), d = (3, 4, 5), so r = (1, 2, 3) + t(3, 4, 5). Setting t = 0 gives A and t = 1 gives B. Split it into parametric equations: x = 1 + 3t, y = 2 + 4t, z = 3 + 5t. To check whether a point lies on the line, solve for t in each equation and confirm all three values match.
Where can you find vector images?
Vector images, made of paths rather than pixels, are available from free libraries such as SVG Repo, Openclipart and Wikimedia Commons, icon sets such as Heroicons and Font Awesome, and stock sites like Freepik and Vecteezy, which have free and paid tiers.
Also asked as: where to find vector images
Check each image's licence: some require attribution, some forbid commercial use, and stock sites have their own terms. Vector formats include SVG, AI, EPS and PDF; SVG works directly on websites and scales without blurring. To create your own, use Inkscape, which is free, Figma, or Adobe Illustrator. In AI image work, note that diffusion models output pixels, so convert generated images to vectors with tracing tools if you need scalable artwork.
Sources
GenAI engineer and AI product builder with 2+ years shipping production-grade AI systems: RAG pipelines, fine-tuned LLMs, hybrid retrieval and multi-modal apps across vision, speech and OCR, architected end to end from ingestion to deployment. Leads engineering for SCULT INDIA's 14-member team, founded the 500+ member TechVerse Enclave community and has mentored 200+ students. Three hackathon first prizes: Changethon 2025 (IIT Roorkee), Product Genesis at Vividhotsava 2025 (CSJMU) and BYTEBATTLE (MeetKats).
Open to GenAI roles, hackathon judging, mentorship sessions and guest talks at colleges. For campus sessions the inviting institution covers the visit end to end: travel (a First AC train ticket for journeys up to five hours, a flight for anything longer), accommodation, meals, and pickup and drop; the honorarium and workshop fees are negotiable on WhatsApp or on the call, and requests are welcome from institutions that can cover the visit this way. Email pranjulrathour41@gmail.com.
