Question

fill in the blank question
in the equation $lambda=cos\theta_xmathbf{i}+cos\theta_ymathbf{j}+cos\theta_zmathbf{k}$, the vector $lambda$ is a vector whose magnitude is equal to
assume the angles $\theta_x$ and $\theta_y$ are acute and $\theta_z$ is obtuse.

Explanation:

Step1: Recall the formula for the magnitude of a vector

The magnitude of a vector $\lambda = a\mathbf{i}+b\mathbf{j}+c\mathbf{k}$ is given by $|\lambda|=\sqrt{a^{2}+b^{2}+c^{2}}$. Here, $a = \cos\theta_{x}$, $b=\cos\theta_{y}$, and $c = \cos\theta_{z}$.

Step2: Apply the formula

$|\lambda|=\sqrt{\cos^{2}\theta_{x}+\cos^{2}\theta_{y}+\cos^{2}\theta_{z}}$. In three - dimensional space, for the direction cosines of a vector, $\cos^{2}\theta_{x}+\cos^{2}\theta_{y}+\cos^{2}\theta_{z}=1$. So, $|\lambda| = 1$.

Answer:

$1$