Search any question & find its solution
Question:
Answered & Verified by Expert
If $|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a} \cdot \mathbf{b}|^{2}=144|\mathbf{a}|=6$, then $|\mathbf{b}|$ is equal to
Options:
Solution:
1363 Upvotes
Verified Answer
The correct answer is:
2
We have,
$|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a} \cdot \mathbf{b}|^{2}=144, \text { and }|\mathbf{a}|=6$
We know that,
$|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a} \cdot \mathbf{b}|^{2}=(|\mathbf{a}||\mathbf{b}|)^{2}$
$\Rightarrow \quad|\mathbf{a}|^{2}|\mathbf{b}|^{2}=144$
$\Rightarrow \quad(6)^{2}|\mathbf{b}|^{2}=144$
$\Rightarrow \quad|\mathbf{b}|^{2}=4$
$\Rightarrow \quad|\mathbf{b}|=2$
$|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a} \cdot \mathbf{b}|^{2}=144, \text { and }|\mathbf{a}|=6$
We know that,
$|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a} \cdot \mathbf{b}|^{2}=(|\mathbf{a}||\mathbf{b}|)^{2}$
$\Rightarrow \quad|\mathbf{a}|^{2}|\mathbf{b}|^{2}=144$
$\Rightarrow \quad(6)^{2}|\mathbf{b}|^{2}=144$
$\Rightarrow \quad|\mathbf{b}|^{2}=4$
$\Rightarrow \quad|\mathbf{b}|=2$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.