Mathematics

Problem

Match the statement of Column I with values of Column II.

Column I	Column II
A. $\mathbf{a} = \mathbf{b} = 2$ , $\mathbf{x} = \mathbf{a} + \mathbf{b}$ , $\mathbf{y} = \mathbf{a} - \mathbf{b}$ <br>If $\mathbf{x} \times \mathbf{y} = 2\{\lambda - (\mathbf{a} \cdot \mathbf{b})^2\}^{1/2}$ , then value of $\lambda$ is	p. 4
B. The non-zero value of $\lambda$ for which angle between $\lambda\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + \lambda\hat{j} + \hat{k}$ is $\frac{\pi}{3}$	q. 42

Column I	Column II
C. The non-zero value of $k$ for which the lines $kx - 4y + 7z + 16 = 0$ <br> $= 4x + 3y - 2z + 3$ and<br> $x - 3y + 4z + 6 = 0 = x - y + z + 1$ <br>are coplanar is	r. 16
D. If $a = b = 1$ and $c = 2$ , then maximum value of<br> $a - 2b ^2 + b - 2c ^2 + c - 2a ^2$ is	s. 7
	t. 5