Question

Avector makes45&60angles with xandy respectively thenthe angle made by it z axis is

Answer 1

$\Large\boxed{\quad\sf{60^o}\quad}$

If a vector makes angles $\alpha,\ \beta$ and $\gamma$ with each axis, then,

$\longrightarrow\sf{\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1}$

Here,

• $\sf{\alpha=45^o}$

• $\sf{\beta=60^o}$

Then,

$\longrightarrow\sf{\cos^245^o+\cos^260^o+\cos^2\gamma=1}$

$\longrightarrow\sf{\dfrac{1}{2}+\dfrac{1}{4}+\cos^2\gamma=1}$

$\longrightarrow\sf{\dfrac{3}{4}+\cos^2\gamma=1}$

$\longrightarrow\sf{\cos\gamma=\dfrac{1}{2}}$

$\Longrightarrow\sf{\underline{\underline{\gamma=60^o}}}$