Question

Find a vector `vec"r"` of magnitude `3sqrt(2)` units which makes an angle of `pi/4` and `pi/2` with y and z-axes, respectively.

Answer 1

Here m = `cos  pi/4 = 1/sqrt(2)` and n = `cos  pi/2` = 0.

Therefore, l² + m² + n² = 1   ...(Gives)

`"l"^2 + 1/2 + 0` = 1

⇒ l = `+- 1/sqrt(2)`

Hence, the required vector `vec"r" = 3sqrt(2) ("l"hat"i" + "m"hat"j" + "n"hat"k")` is given by

`vec"r" = 3sqrt(2) (+- 1/sqrt(2) hat"i" + 1/sqrt(2) hat"j" + 0hat"k")`

= `vec"r" = +- 3hat"i" + 3hat"j"`.