Vector Algebra Question 46
Question: If If $|\vec{a}|=3,|\vec{b}|=4$ and the angle between $\vec{a}$ and $\vec{b}$ be $120^{\circ}$, then $|4 \vec{a}+3 \vec{b}|=$
Options:
A) 25
B) 12
C) 13
D) 7
Show Answer
Answer:
Correct Answer: B
Solution:
- $ |4\mathbf{a}+3\mathbf{b}|=\sqrt{(4\mathbf{a}+3\mathbf{b}).(4\mathbf{a}+3\mathbf{b})} $ $ =\sqrt{16|\mathbf{a}{{|}^{2}}+9|\mathbf{b}{{|}^{2}}+24\mathbf{a}.\mathbf{b}} $ $ =\sqrt{144+144+24\times 3\times 4\times ( \frac{-1}{2} )}=12. $
BETA
