Question

Given vector A=i-2j-3k and vector B=4i-2j+6k. What is the angle made by A+B with x-axis?

Answer 1

See below.

Explanation:

`vec A+vec B = 5 hat i-4hat j+3 hat k`

`X`-axis can be represented as `hat i`

now, given two non null vectors `vec a, vec b` we have

`<< vec a, vec b >> = norm(vec a)*norm(vec b) cos(hat(vec a, vec b))` or

`cos(hat(vec a, vec b)) = (<< vec a, vec b >> )/(norm(vec a)*norm(vec b) )`

now making `vec a = 5 hat i-4hat j+3 hat k` and `vec b = hat i` we have

`cos(hat(vec A+vec B, hat i)) = 5/(1*sqrt(5^2+4^2+3^2)) = sqrt(2)/2` so the angle is `pi/4` or `45^@`