Vector Algebra Question 76
Question: If $ \vec{a}=2\hat{i}+2\hat{j}+3\hat{k},\vec{b}=-\hat{i}+2\hat{j}+\hat{k} $ and $ \overrightarrow{c}=3\hat{i}+\hat{j} $ are three vectors such that $ \vec{a}+t\vec{b} $ is perpendicular to $ \vec{c} $ , then what is t equal to?
Options:
A) 8
B) 6
C) 4
D) 2
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ \vec{a}+t\vec{b}=(2-t)\hat{i}+(2+2t)\hat{j}+(3+t)\hat{k} $ $ (\vec{a}+t\vec{b}) $ and $ \vec{c} $ is perpendicular. Therefore, $ (\vec{a}+t\vec{b}).\vec{c}=0 $ $ 3(2-t)+2+2t=0 $ $ 6-3t+2t+2=0 $ $ t=8 $
BETA
