Vector Algebra Question 303
Question: If $ (x,y,z)\ne (0,0,0) $ and $ (\mathbf{i}+\mathbf{j}+3,\mathbf{k}),x+(3,\mathbf{i}-3\mathbf{j}+\mathbf{k}),y $ $ +(-4\mathbf{i}+5\mathbf{j}),z=\lambda ,(x\mathbf{i}+y\mathbf{j}+z\mathbf{k}), $ then the value of l will be
[IIT 1982; RPET 1984]
Options:
A) 2, 0
B) 0, ? 2
C) 1, 0
D) 0, ? 1
Show Answer
Answer:
Correct Answer: D
Solution:
- Comparing the coefficients of $ \mathbf{i},\mathbf{j} $ and $ \mathbf{k}, $ the corresponding equations are $ x+3y-4z=\lambda x $ or $ (1-\lambda )x+3y-4z=0 $ ……(i) $ x-(\lambda +3)y+5z=0 $ ……(ii) $ 3x+y-\lambda z=0 $ …..(iii) These equations (i), (ii) and (iii) have a non-trivial solution, if $ \begin{vmatrix} (1-\lambda ) & 3 & -4 \\ 1 & -(\lambda +3) & 5 \\ 3 & 1 & -\lambda \\ \end{vmatrix} =0\Rightarrow \lambda =0,-1. $
BETA
