Vectors Question 205
Question: Obtain the directions of vector $ (\vec{A},-\vec{B}), $ if $ \vec{A}=2\hat{i}+3\hat{j}=,\hat{k},\vec{B},=2\hat{i}+2\hat{j}+3\hat{k} $
Options:
A) $ 0,,\frac{1}{\sqrt{5}},,,\frac{-2}{\sqrt{5}} $
B) $ 0,,\frac{1}{\sqrt{5}},,,\frac{1}{\sqrt{5}} $
C) 0, 0, $ \frac{1}{\sqrt{5}} $
D) None of these
Correct Answer: A [a] $ (\vec{A}-\vec{B})=\sqrt{1+4}=\sqrt{5} $
$ (\vec{A}-\vec{B})=,2\hat{i}+3\hat{j}+,\hat{k},-2\hat{i}-2\hat{j}-3\hat{k} $
$ =\hat{j}-2\hat{k} $
$ |\vec{A}-\vec{B}|=\sqrt{1+4}=,\sqrt{5} $
Direction cosine $ =,\frac{0}{\sqrt{5}},,\frac{1}{\sqrt{5}},,-\frac{2}{\sqrt{5}} $
i.e., $ =,0,,\frac{1}{\sqrt{5}},,-\frac{2}{\sqrt{5}} $ .
Show Answer
Answer:
Solution:
BETA
