Vector Algebra Question 312
Question: If $ a=(1,,-1,,2),\ b=(-2,,3,,5) $ , $ \mathbf{c}=(2,,,-2,,4) $ and i is the unit vector in the x-direction, then $ (a-2b+3c),.,i= $
[Karnataka CET 2001]
Options:
A) 11
B) 15
C) 18
D) 36
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \mathbf{a}=(1,,-1,,2),\mathbf{b}=(-,2,,3,,5),,\mathbf{c}=(2,,-2,,4) $ So, $ \mathbf{a}=(1,-1,2)\equiv \mathbf{i}-\mathbf{j}+2\mathbf{k};\mathbf{b}=(-2,3,5)\equiv -,2\mathbf{i}+3\mathbf{j}+5\mathbf{k} $ and $ \mathbf{c}=(2,-2,4)\equiv 2\mathbf{i}-2\mathbf{j}+4\mathbf{k} $
$ \Rightarrow \mathbf{a}-2\mathbf{b}+3\mathbf{c}=(\mathbf{i}-\mathbf{j}+2\mathbf{k})-2(-2\mathbf{i}+3\mathbf{j}+5\mathbf{k}) $ $ +3(2\mathbf{i}-2\mathbf{j}+4\mathbf{k}) $ $ =11\mathbf{i}-13\mathbf{j}+4\mathbf{k} $ and $ (\mathbf{a}-2\mathbf{b}+3\mathbf{c}),.,\mathbf{i}=11. $
BETA
