Question

Find a • b.

a = 4i + 8j, b = -2i + 3j

Answer 1

this is the 'dot' product of 2 vectors
a . b = 4i*-2i + 8j*3j

Answer 2

its also called the Scalar product

Answer 3

can you simplify this further?

Answer 4

the square of the unit vectors i and j both = 1

Answer 5

Okay. hmm

Answer 6

-8,24

Answer 7

@welshfella

Answer 8

@xamr Almost, but the dot product gives you a single value not a pair of values. So you need to ad those two numbers together.

One application of the dot product is to calculate length which is the square root of the dot product,

$$\text{length of vector a} = \sqrt{\vec a \cdot \vec a }$$

Answer 9

So 16

Answer 10

Yep

Answer 11

yes

Answer 12

By thinking of i,j,k as components x,y,z we can rewrite vectors a and b.
\[\vec a = \langle 4~,~8\rangle ~,~ \vec b = \langle -2~,~ 3\rangle\]

Answer 13

Thank you all.

Answer 14

yw

Answer 15

when you dot a vector with another vector, you get the amount of projection of one vector onto another. So if two vectors are at right angles to each other, then there's no projection at all, and the dot product is zero

$$\vec a \cdot \vec b = 0 $$ means they're perpendicular to each other