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 points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4), and D(8, 14, 12). Which of the following statements is/are correct?

1. The points are the vertices of a rectangle ABCD.

2. The mid-point of A C is the same as that of BD.

Select the correct answer using the code given below :