Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A vector $\vec{a}$ is parallel to the line of intersection of the plane determined by the vectors $\mathrm{\hat{i}, \hat{i}+\hat{j}}$ and the plane determined by the vectors $\mathrm{\hat{i}-\hat{j}, \hat{i}+\hat{k}}$ . The obtuse angle between $\vec{a}$ and the vector $\mathrm{ \vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}}$ is
Option: 1
$\mathrm{\frac{3 \pi}{4}}$

Option: 2
$\frac{2 \pi}{3}$

Option: 3
$\frac{4 \pi}{5}$

Option: 4
$\frac{5 \pi}{6}$

Answers (1)

best_answer

$\mathrm{\overrightarrow{n_{1}} =i \times(i+j)=i \times i+i \times j=0+k=k} \\$

$\mathrm{\overrightarrow{n_{2}} =(i-j) \times(i+k)} \\$

$\mathrm{=i \times i+i \times k-j \times i-j \times k} \\$

$\mathrm{=-j+k-i} \\$

$\mathrm{=-i-j+k}$

$\mathrm{\therefore \overrightarrow{a} \text { is parallel to } \overrightarrow{n}_{1} \times \overrightarrow{n}_{2}}$

$\mathrm{=\left|\begin{array}{rrr} i & j & k \\ 0 & 0 & 1 \\ -1 & -1 & 1 \end{array}\right|} \\$

$\mathrm{=i-j}$

$\mathrm{Angle\; between \overrightarrow{a} and \overrightarrow{b}}$

$\mathrm{\cos \theta =\frac{\vec{a} \cdot \overrightarrow{b}}{| \overrightarrow{a}|| \overrightarrow{b}|}} \\$

$\mathrm{=\frac{(i-j) \cdot(i-2 j+2 k)}{\sqrt{2} \cdot 3}} \\$

$=\frac{1}{\sqrt{2}} \\$

$\mathrm{\therefore \text { obtuse angle }=\frac{3 \pi}{4} }$

Hence correct option is 1

Posted by

Rishabh

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

JEE Main 2025: 11 from Kota coaching centres among 24 students with 100 percentile

anam-khan

Low JEE Main rank? Explore alternative paths for engineering admission

anam-khan

Gender-gap in JEE Main 2025: Female participation remains around 31%, overall pool drops by 7.09%

Latest Question