425 views

What is dot product and how to calculate it?

There are two ways of multiplying vectors: one gives you another vector (cross product) and the other gives you a scalar- a number, like 3, 18 or 196 352. Hence, dot product is also called the scalar product.

Imagine two vectors X=(a, b, c) and Y=(d, e, f). The first number gives you length of the vector in the x direction, second tells you its length in the y direction and third gives you the z direction. The easiest way to find the dot product is done by multiplying the numbers in the i, j and k rows of both vectors and then adding the results together. So, on the example of X and YX.Y=ad+be+cf.

Another example: A=(1, 5, 9) and B=(0, -6, 4). The dot product of A and BA.B= 1*0 + (5*-6) + (4*9) = 0 - 30 + 36 =6.

Dot product can also be used to find the angle between two vectors. The full formula for dot product between X and is: X.Y = |X| |Y| cos(x). Where 'x' is the angle between both vectors and |X| and |Y| are the lengths of vectors X and Y. The length can be found using the formula: |X| = sqrt(a2+b2+c2).

11 months ago

Answered by Filip, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

434 SUBJECT SPECIALISTS

£20 /hr

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi! I am studying Mathematics at Bath University and I am passionate about teaching, and learning mathematics.”

MyTutor guarantee

|  1 completed tutorial

£26 /hr

Degree: Mathematics (Masters) - York University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I study Maths at York University; I chose York because I loved the lecturers, they made maths fun and easy- that's what I hope to do with all my students!”

£22 /hr

Degree: Economics (Bachelors) - Cambridge University

Subjects offered:Maths, Economics+ 2 more

Maths
Economics
-Personal Statements-
-Oxbridge Preparation-

“Economics Graduate from Cambridge, wanting to share my passion for the discipline”

Currently unavailable: for new students

Degree: MSci Chemical Physics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Chemistry
Biology

“My name is Filip and I'm a 4th year student of Chemical Physics at Bristol Uni. I'm quite chatty, friendly and find science really exciting!”

You may also like...

Posts by Filip

Resolving the forces for an object suspended on two strings.

What are the rules for decomposition of partial fractions?

What is dot product and how to calculate it?

Other A Level Maths questions

Differentiate The Following function

How can I calculate the maximum value of the compound angle formulae Rsin(x+a) and Rcos(x+a)?

Some videos I've made

A particle of mass 0.8 kg moving at 4 m/s rebounds of a wall with coefficient of restitution 0.3. How much Kinetic energy is lost?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.