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 :

Consider the equation of a sphere x2 + y2 + z2 − 4x − 6y − 8z − 16 = 0.

Which of the following statements is/are correct ?

1. z-axis is tangent to the sphere.

2. The centre of the sphere lies on the plane x + y + z − 9 = 0.

Select the correct answer using the code given below :

A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?