Find a vector (a) of magnitude 5root2 making an angle of pie/4 with x axis pie/2 with y axis and an acute angle k with z axis
Hello Srishti, the condition is that the sum of squares of directions cosines such cos α, cos β and cos γ is to be 1
So cos^2 pi/4 + cos^2 pi/2 + cos^2 γ = 1
==> 1/2 + 0 + cos^2 γ = 1
==> cos^2 γ= 1/2
So γ = pi/4
The magnitude is given as 5√2
Hence components along the axes are 5√2 cos pi/4 , 5√2 cos pi/2 and 5√2 cos pi/4
So the expected vector will be 5 i + 5 j
So cos^2 pi/4 + cos^2 pi/2 + cos^2 γ = 1
==> 1/2 + 0 + cos^2 γ = 1
==> cos^2 γ= 1/2
So γ = pi/4
The magnitude is given as 5√2
Hence components along the axes are 5√2 cos pi/4 , 5√2 cos pi/2 and 5√2 cos pi/4
So the expected vector will be 5 i + 5 j