Vector Algebra Question 380
Question: If $ \mathbf{a}=2,\mathbf{i}+2,\mathbf{j}+3,\mathbf{k},\mathbf{b}=-\mathbf{i}+2,\mathbf{j}+\mathbf{k} $ and $ c=3,\mathbf{i}+\mathbf{j}, $ then $ \mathbf{a}+t,\mathbf{b} $ is perpendicular to c if $ t= $
[MNR 1979; MP PET 2002]
Options:
A) 2
B) 4
C) 6
D) 8
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \mathbf{a}+t\mathbf{b}=2\mathbf{i}+2\mathbf{j}+3\mathbf{k}+(-t\mathbf{i}+2t\mathbf{j}+t\mathbf{k}) $ $ =(2-t)\mathbf{i}+(2+2t)\mathbf{j}+(3+t)\mathbf{k} $ Given that it is perpendicular to $ \mathbf{c}=3\mathbf{i}+\mathbf{j} $ Hence $ (2-t)3+(2+2t)1+(3+t)0=0 $
$ \Rightarrow 6-3t+2+2t=0\Rightarrow t=8. $
BETA
