Vector Algebra

For real numbers , , , and , consider the matrix M = bmatrix & 1 2 & - 1 2 \ 1 3 & & 1 3 \ & & bmatrix . Suppose that MMT = I , where MT is the transpose of the matrix M, and I is the 3 3 identity matrix. Let u = i + 1 3 j + k , v = 1 2 i + j + k and w = - 1 2 i + 1 3 j + k . Match each entry in List-I to the correct entry in List-II and choose the correct option.

1. (P) → (5), (Q) → (4), (R) → (2), (S) → (1)
2. (P) → (4), (Q) → (5), (R) → (1), (S) → (2)
3. (P) → (5), (Q) → (3), (R) → (2), (S) → (1)
4. (P) → (5), (Q) → (4), (R) → (1), (S) → (2)

Let w = i + j - 2 k, and u and v be two vectors, such that u v = w and v w = u. Let , , , and t be real numbers such that u = i + j + k, -t + + = 0, - t + = 0, and + - t = 0. Match each entry in List-I to the correct entry in List-II and choose the correct option.

1. (P) → (2), (Q) → (1), (R) → (4), (S) → (5)
2. (P) → (2), (Q) → (4), (R) → (3), (S) → (5)
3. (P) → (2), (Q) → (1), (R) → (4), (S) → (3)
4. (P) → (5), (Q) → (4), (R) → (1), (S) → (3)