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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.
Solution
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"`.
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