Question

6. Vector A makes equal angles with x, y and z axis. Value
of its components (in terms of magnitude of A) will be
(A)A/√3
(B)A√2
(C)√3A
(D)√3/A​

Answer 1

let vector a make ¢ angle with x , y ,z axes .

according to direction cosine ,

cos^2¢ +cos^2¢ +cos^2¢ =1

3cos^2¢ =1

take square root both side 

√3cos¢ = +_ 1

so, ¢ =cos^-1(+_1/√3) = cos^-(1/√3)

now , 

x -component = cos^-1(1/√3)

y -component =cos^-1(1/√3)

z -component =cos^-1(1/√3)

Answer 2

we know that vector in three dimensions makes an angle

i.e. cos^2x+cos^2y+cos^2z = 1

as, x=y=z

cos^2x = 1/3

cos x=1/√3

So, Value

of its components (in terms of magnitude of A) will be A/√3

Hope it helps