Consider the following for the next two (02) items that follow :

Let A(1, -1, 2) and B(2, 1, -1) be the end points of the diameter of the sphere

x² + y² + z² + 2ux + 2vy + 2wz - 1 = 0.  

P(x, y, z) is any point on the sphere, then what is PA² + PB² equal to ?  

Consider the following for the next two (02) items that follow :

Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5). They are inclined at an angle $\frac{\pi}{4}$

What is the value of k? 

Consider the following for the next two (02) items that follow :

Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5). They are inclined at an angle $\frac{\pi}{4}$

What are the direction ratios of a line which is perpendicular to both the lines ?

Consider the following for the next two (02) items that follow :

Let $\vec{a}=3 \hat{i}+3 \hat{j}+3 \hat{k} $ and $ \vec{c}=\hat{j}-\hat{k} \text {. Let } \vec{b}$ be such that $\vec{a} \cdot \vec{b}=27 $ and $ \vec{a} \times \vec{b}=\overrightarrow{9 c}$

What is $\vec{b}$ equal to ?