The given vector is V = ai + bj + ck

a=0, b=1, c=1

also $|\overline{V}|=\sqrt{a^{2}+b^{2}+c^{2}}$

Step 1: Rotation of vector V about X-axis by an angle $\theta =+\theta_1$ {+ve indicates CCW}

Now, $, \mathrm{V}_{1}=\mathrm{b}_{j}+\mathrm{ck}$

Also,

$1\left(\mathrm{V}_{1}\right)=\sqrt{\mathrm{b}^{2}+\mathrm{c}^{2}}$

From figure, $\sin \theta_{1}=\mathrm{b} / \sqrt{\mathrm{b}^{2}+\mathrm{c}^{2}}$

$\cos \theta_{1}=\mathrm{c} / \sqrt{\mathrm{b}^{2}+\mathrm{c}^{2}}$

Let, $\sqrt{b^{2}+c^{2}}=\lambda$

So, …