Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let be two vectors such that <img alt="\mathrm{}|\vec{a}+\vec{b}|^{2}=|\vec

Let \mathrm{}\vec{a}$ and $\vec{b} be two vectors such that \mathrm{}|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3$ and $|\vec{a} \times \vec{b}|^{2}=75. Then \mathrm{}|\vec{a}|^{2} is equal to_________.

Option: 1

14


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} &\mathrm{|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}}\\ &\Rightarrow \mathrm{|\vec{a}|^{2}+|\vec{b}|^{2}+2\vec{a}.\vec{b}^{2}}=|\vec{a}|^{2}+2|\vec{b}|^{2}\\ &\Rightarrow \mathrm{|\vec{b}|^{2}=+2|\vec{a}|.|\vec{b}|^{2}=6}\\ &\mathrm{\Rightarrow |\vec{b}|=\sqrt{6}}\\ \end{aligned}

\begin{aligned} &\mathrm{|\vec{a}.\vec{b}|^{2}+|\vec{a} \times \vec{b}|^{2}=|\vec{a}|^{2}|b|^{2}}\\ &\mathrm{\Rightarrow 9+75=|\vec{a}|^{2}.6}\\ &\mathrm{\Rightarrow |\vec{a}|^{2}=\frac{84}{6}=14 } \end{aligned}

Posted by

seema garhwal

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Faridabad: 17-year-old girl preparing for JEE Main 2026 dies by suicide
anam-khan

NTA JEE Mains 2026 application closes at 9 am today; correction facility from December 1
anam-khan

JEE Main 2026 Registration LIVE: NTA session 1 correction facility opens on December 1; exam pattern, cut-offs

Latest Question