Vector Algebra Question 330
Question: The direction cosines of the vector $ 3\mathbf{i}-4\mathbf{j}+5\mathbf{k} $ are
[Karnataka CET 2000]
Options:
A) $ \frac{3}{5},,\frac{-4}{5},\frac{1}{5} $
B) $ \frac{3}{5\sqrt{2}},,\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}} $
C) $ \frac{3}{\sqrt{2}},,\frac{-4}{\sqrt{2}},,\frac{1}{\sqrt{2}} $
D) $ \frac{3}{5\sqrt{2}},\frac{4}{5\sqrt{2}},,\frac{1}{\sqrt{2}} $
Show Answer
Answer:
Correct Answer: B
Solution:
- Vector $ \overrightarrow{A}=3i-4j+5k $ . We know that direction cosines of $ \overrightarrow{A} $ $ =\frac{3}{\sqrt{3^{2}+4^{2}+5^{2}}},,\frac{-4}{\sqrt{3^{2}+4^{2}+5^{2}}},,\frac{5}{\sqrt{3^{2}+4^{2}+5^{2}}} $ $ =\frac{3}{5\sqrt{2}},,\frac{-4}{5\sqrt{2}},,\frac{1}{\sqrt{2}} $ .
BETA
