Components of a vector

Question

If I have the angle between two vectors, and I have the components $(x,y,z)$ of the first vector $( xi + yj + zk)$, how can I know the components $(x',y',z')$ of the second vector ?

Answer 1

Set of all the values of x, y, z satisfying following equation is your solution,

since, $\cos\alpha=\dfrac{v\cdot u}{|v|\cdot|u|}$

$\cos\alpha=\dfrac{xx_1+yy_1+zz_1}{\sqrt{x^2+y^2+z^2}\sqrt{x_1^2+y_1^2+z_1^2}}$

Answer 2

Taketheir dot product then all values of $x$, $y$, $z$ satisfying resulting equation is your answer.