Vector Algebra Question 31
Question: What is a vector of unit length orthogonal to both the vectors $ \hat{i}+\hat{j}+\hat{k} $ and $ 2\hat{i}+3\hat{j}-\hat{k} $ ?
Options:
A) $ \frac{-4\hat{i}+3\hat{j}-\hat{k}}{\sqrt{26}} $
B) $ \frac{-4\hat{i}+3\hat{j}+\hat{k}}{\sqrt{26}} $
C) $ \frac{-3\hat{i}+2\hat{j}-\hat{k}}{\sqrt{14}} $
D) $ \frac{-3\hat{i}+2\hat{j}+\hat{k}}{\sqrt{14}} $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ \vec{A}=\hat{i}+\hat{j}+\hat{k} $ $ \vec{B}=2\hat{i}+3\hat{j}-\hat{k} $ $ \vec{A}\times \vec{B}= \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 1 & 1 \\ 2 & 3 & -1 \\ \end{vmatrix} $ $ =\hat{i}(-1-3)-\hat{j}(-1-2)+\hat{k}(3-2) $ $ =-4\hat{i}+3\hat{j}+\hat{k} $ Vector of unit length orthogonal to both the vectors $ \overset{\to }{\mathop{A}}, $ and $ \overset{\to }{\mathop{B}}, $ $ =\frac{\overset{\to }{\mathop{A}},\times \overset{\to }{\mathop{B}},}{|\overset{\to }{\mathop{A}},\times \overset{\to }{\mathop{B}},|} $ $ =\frac{-,4i+3j+k}{\sqrt{16+9+1}}=\frac{-,4\hat{i}+3\hat{j}+\hat{k}}{\sqrt{26}} $
BETA
