If and makes an angle with each other, then for . The integer value of is

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
If $\vec{a}$ and $\vec{b}$ makes an angle $\cos^{- 1} (\frac{5}{9})$ with each other, then $| \vec{a} + \vec{b} | = \sqrt{2} | \vec{a} - \vec{b} |$ for $| \vec{a} | = n | \vec{b} |$ . The integer value of $n$ is __________ . [2024]

Ans.
(3)    $| \vec{a} + \vec{b} | = \sqrt{2} | \vec{a} - \vec{b} |$

   $a^{2} + b^{2} + 2 a b \cos θ = 2 (a^{2} + b^{2} - 2 a b \cos θ)$

   $n^{2} b^{2} + b^{2} + 2 n b^{2} \times \frac{5}{9} = 2 n^{2} b^{2} + 2 b^{2} - 4 n b^{2} \times \frac{5}{9}$

   $n^{2} + 1 + \frac{10 n}{9} = 2 n^{2} + 2 - \frac{20 n}{9}$

   $9 n^{2} - 30 n + 9 = 0 \Rightarrow n = 3, \frac{1}{3}$

Integer value $n = 3$

Want Us to Email you About Special Offers & Updates?