Question

What is the cosine of the angle which the vector √2 i + j + k makes with y axis

Answer 1

A = √2 i + j + k

Direction cosine for y - axis is

$\dfrac{b}{ \sqrt{( {a}^{2} + {b}^{2} + {c}^{2} ) } } = m \: = cos \: \beta$

where a = √2 ; b = 1 ; c = 1

$cos \: \beta = \dfrac{1}{( \sqrt{(2 + 1 + 1)} } = \dfrac{1}{2}$


Therefore , $\beta = \dfrac{\pi}{3}$