Vector Algebra Question 164
Question: Let $ \mathbf{a}=\mathbf{i} $ be a vector which makes an angle of $ 120^{o} $ with a unit vector b. Then the unit vector $ (\mathbf{a}+\mathbf{b}) $ is
[MP PET 1991]
Options:
A) $ -\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j} $
B) $ -\frac{\sqrt{3}}{2}\mathbf{i}+\frac{1}{2}\mathbf{j} $
C) $ \frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j} $
D) $ \frac{\sqrt{3}}{2}\mathbf{i}-\frac{1}{2}\mathbf{j} $
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Answer:
Correct Answer: C
Solution:
- $ \mathbf{b}=\cos 120{}^\circ \mathbf{i}+\sin 120{}^\circ \mathbf{j} $ or $ \mathbf{b}=-\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j}. $ Therefore $ \mathbf{a}+\mathbf{b}=\mathbf{i}-\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j}=\frac{1}{2}\mathbf{i}+\frac{\sqrt{3}}{2}\mathbf{j} $ .
BETA
