Question

If `vec(a) = 2hat(i) + 3hat(j) - 6hat(k)` and `vec(b) = 12 hat(j) + 5 hat(k)`. then (projection of `vec(a)` on `vec(b)//("projection of b on a")` )
A. `7//13`
B. `13//7`
C. `20//13`
D. `13//20`

Answer 1

Correct Answer - A
`vec(a) .vec(b) = ab cos theta`
projection of `vec(a)` on `vec(b) = a cos theta = (vec(a).vec(b))/(b)`
projection of `vec(b)` on `vec(a) = b cos theta = (vec(a).vec(b))/(a)`
`("projection of" vec(a) "on" vec(b))/("projection of"vec(b) "on" vec(a)) = ((vec(a).vec(b))/(b))/((vec(a).vec(b))/(a))`
`= (a)/(b) = (7)/(13)`