What is the cosine of the angle which the vector âˆš2 i + j + k makes with y-axis - Maths - Three Dimensional Geometry

Question

What is the cosine of the angle which the vector
âˆš2 i + j + k makes with y-axis

Ajanta Trivedi · Accepted Answer

for a vector $a i + b j + c k$ direction cosinesare given by: $l = \frac{a}{\sqrt{a^{2} + b^{2} + c^{2}}}, m = \frac{b}{\sqrt{a^{2} + b^{2} + c^{2}}}, n = \frac{c}{\sqrt{a^{2} + b^{2} + c^{2}}}$

$l = \cos α, m = \cos β, n = \cos γ$ , where $α, β, γ$ are angles made by the vectors with x-axis , y-axis and z-axis respectively.

for the given vector √2 i + j + k , $m = \cos β = \frac{1}{\sqrt{2 + 1 + 1}} = \frac{1}{\sqrt{4}} = \frac{1}{2}$

therefore $β = \frac{π}{3}$

thus angle made with y-axis is 60 deg.

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