Position vector of a point A is (a \stackrel{\^}{i}+b \stackrel{\^}{j}+c {k^{\^}}) and a^{2}+b^{2}+c^{2}=4 ; and position vector of another point {B} is (p \stackrel{\^}{i}+q \stackrel{\^}{j}+r {k^{\^}}) and p^{2}+q^{2}+r^{2}=9. Given \\angleA O B=2 \cos ^{-1} \frac{1}{5}, where {O} is origin. If A Q is perpendicular to angle bisector of \\angleA O B i.e. line OQD where D lies on A B, then value of 25 |Q D|=?

JEE Advanced 2021 Full Test 3 Paper 2

SECTION – B (Single Digit Integer Type)
This section contains 06 questions. The answer to each question is a Single Digit integer ranging from 0 to 9, both inclusive.

Question : 45 of 54

Marks: +1, -0

Position vector of a point A is (a

) and a2+b2+c2=4; and position vector of another point B is (p

) and p2+q2+r2=9. Given ∠AOB=2cos−1

, where O is origin. If AQ is perpendicular to angle bisector of ∠AOB i.e. line OQD where D lies on AB, then value of 25|QD|=?

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