Vector Algebra Question 124
Question: If $ \mathbf{p}=\mathbf{i}-2\mathbf{j}+3\mathbf{k} $ and $ \mathbf{q}=3\mathbf{i}+\mathbf{j}+2\mathbf{k}, $ then a vector along r which is linear combination of p and q and also perpendicular to q is
[MNR 1986]
Options:
A) $ \mathbf{i}+5\mathbf{j}-4\mathbf{k} $
B) $ \mathbf{i}-5\mathbf{j}+4\mathbf{k} $
C) $ -\frac{1}{2},(\mathbf{i}+5\mathbf{j}-4\mathbf{k}) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \mathbf{r}=\mathbf{p}+\lambda ,\mathbf{q}\Rightarrow \mathbf{r},.,\mathbf{q}=\mathbf{p},.,\mathbf{q}+\lambda ,\mathbf{q},.,\mathbf{q} $
$ \Rightarrow 0=7+14\lambda \Rightarrow \lambda =-\frac{1}{2} $ Therefore, $ \mathbf{r}=-\frac{1}{2}(\mathbf{i}+5\mathbf{j}-4\mathbf{k}). $
BETA
