A unit vector of modulus 2is equally inclined to `x`- and `y`-axes angle at an angle `pi//3`. Find the length ofprojection of the vector on the `z`-axis.

A unit vector of modulus 2is equally inclined to `x`- and `y`-axes ang

1.	A unit vector of modulus 2is equally inclined to `x`- and `y`-axes angle at an angle `pi//3`. Find the length ofprojection of the vector on the `z`-axis.
Answer» Given that the vector is inclined at an angle `pi//3` with both x- and y-axes. Then `" "cosalpha=cosbeta=(1)/(2)` Also we know that `cos^(2)alpha +cos^(2)beta+cos^(2)gamma=1`. Therefore, `" "cos^(2)gamma=(1)/(2)` or `" "cosgamma=pm(1)/(sqrt(2))` Thus, the given vector is `" "2(cosalphahati+cosbetahatj+cosgammahatk)=2((hati)/(2)+(hatj)/(2)pm(hatk)/(sqrt(2)))=hati+hatjpmsqrt(2)hatk` Hence, the length of projection of vector on the z-axis is `sqrt(2)` units.

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A unit vector of modulus 2is equally inclined to `x`- and `y`-axes angle at an angle `pi//3`. Find the length ofprojection of the vector on the `z`-axis.

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