If P , Q , R and S are the points with position vectors hat i + hat j - hat k , 2 hat i - hat j +3 hat k , 2 hat i -3 hat k and 3 hat i -2 hat j + hat k respectively, then the angle between P Q and R S is

Question

If P , Q , R and S are the points with position vectors hat i + hat j - hat k , 2 hat i - hat j +3 hat k , 2 hat i -3 hat k and 3 hat i -2 hat j + hat k respectively, then the angle between P Q and R S is (A) 0 (B) (π/2) (C) π (D) (π/3)

Tardigrade Admin · Accepted Answer

Given position vectors O P = hat i + hat j - hat k O Q =2 hat i - hat j +3 hat k O R =2 hat i -3 hat k and O S =3 hat i -2 hat j + hat k So P Q = O Q - O P = hat i -2 hat j +4 hat k and R S = O S - O R = hat i -2 hat j +4 hat k As (a1/a2)=(b1/b2)=(c1/c2) ∴ Angle between P Q and RS is 0.

Q. If $P, Q, R$ and $S$ are the points with position vectors $\hat{i} + \hat{j} - \hat{k}, 2 \hat{i} - \hat{j} + 3 \hat{k}, 2 \hat{i} - 3 \hat{k}$ and $3 \hat{i} - 2 \hat{j} + \hat{k}$ respectively, then the angle between $PQ$ and $RS$ is

0

$\frac{π}{2}$

$π$

$\frac{π}{3}$

Q. If P,Q,R and S are the points with position vectors i^+j^​−k^,2i^−j^​+3k^,2i^−3k^ and 3i^−2j^​+k^ respectively, then the angle between PQ and RS is

0

2π​

π

3π​

Given position vectors OP=i^+j^​−k^ OQ=2i^−j^​+3k^ OR=2i^−3k^ and OS=3i^−2j^​+k^ So PQ=OQ−OP=i^−2j^​+4k^ and RS=OS−OR=i^−2j^​+4k^ As a2​a1​​=b2​b1​​=c2​c1​​ ∴ Angle between PQ and RS is 0.

Q. If $P, Q, R$ and $S$ are the points with position vectors $\hat{i} + \hat{j} - \hat{k}, 2 \hat{i} - \hat{j} + 3 \hat{k}, 2 \hat{i} - 3 \hat{k}$ and $3 \hat{i} - 2 \hat{j} + \hat{k}$ respectively, then the angle between $PQ$ and $RS$ is

$\frac{π}{2}$

$π$

$\frac{π}{3}$