Question

Will Reward Medal

Find the inner product of a and b if a=(3,0,-1) and b=(4,-2,5) and state whether the vectors are perpendicular.

Answer 1

\[a\cdot b = |a||b|cos\theta\]

Answer 2

multiply and add

Answer 3

and cos(90)=?

Answer 4

inner product in 3 space = dot product
do you know how to compute the dot product?

Answer 5

No, can you help?

Answer 6

sure \[<x_1,x_2,x_3>\cdot <y_1,y_2,y_3>=x_1y_1+x_2y_2+x_3y_3\]

Answer 7

in your case you got \[3\times 4+0\times (-2)+(-1)\times 5\]

Answer 8

So just multiply that, right?

Answer 9

yeah multiply then add

Answer 10

Add what?

Answer 11

-125 is right?

Answer 12

@satellite73

Answer 13

\[12-5\ne-125\] here a_1=3,b_1=4,... etc\[<a_1,a_2,a_3>\cdot <b_1,b_2,b_3>=a_1b_1+a_2b_2+a_3b_3\]