Q29. Match List-I with List-II and select the correct code. List-I List-II (P) Given a = 2 i ^ + k ^ , b = i ^ + j ^ + k ^ , c = 4 i ^ − 3 j ^ + 7 k ^ , x × b = c × b , x ⋅ a = 0 , find x − c (1)

Question

Q29. Match List-I with List-II and select the correct code.

List-I	List-II
(P) Given $a = 2 \hat{i} + \hat{k}, b = \hat{i} + \hat{j} + \hat{k}, c = 4 \hat{i} - 3 \hat{j} + 7 \hat{k}, x \times b = c \times b, x \cdot a = 0$ , find $x - c$	(1) $\frac{1}{7} (5 \hat{i} + 17 \hat{j})$
(Q) Given $a = \hat{i} + 2 \hat{j}, b = 2 \hat{i} - \hat{k}, x \times a = b \times a, x \times b = a \times b$ , find $14 x /∣ x ∣$	(2) $\hat{i} - \frac{7}{5} \hat{j} + \frac{1}{5} \hat{k}$
(R) On segment AB, where $O A = \hat{i} - 2 \hat{j} + \hat{k}, OB = \hat{i} + \hat{j} - 3 \hat{k}$ , find the position vector one unit from A.	(3) $3 \hat{i} + 2 \hat{j} - \hat{k}$
(S) Two triangle vertices are $- \hat{i} + 3 \hat{j}$ and $2 \hat{i} + 5 \hat{j}$ , and the orthocentre is $\hat{i} + 2 \hat{j}$ ; find the third vertex.	(4) $- 5 \hat{i} + \hat{j} + \hat{k}$

TestHub · Accepted Answer

(P) x − c = t b and x ⋅ a = 0 give t = − 5 , hence (4). (Q) x ∥ ( a + b ) = 3 i ^ + 2 j ^ ​ − k ^ , hence (3). (R) Move one unit from A toward B: O A + ( OB − O A ) /5 = i ^ − 5 7 ​ j ^ ​ + 5 1 ​ k ^ , hence (2). (S) Altitude conditions give the third vertex 7 1 ​ ( 5 i ^ + 17 j ^ ​ ) , hence (1). Therefore code A.

Mathematics - Vector Question with Solution | TestHub

Options:

Doubts & Discussion