Answer:
Option C
Explanation:
position vector of P= aˆi+bˆj+cˆk
Position vector of Q= bˆi+cˆj+aˆk
Position vector R=cˆi+aˆj+bˆk
Now, PQ= PV of Q-PV of P
=(bˆi+cˆj+aˆk)-(aˆi+bˆj+cˆk)

=(b−a)ˆi+(c−b)ˆj+(a−c)ˆk
Similarly, PR= (c−a)ˆi+(a−b)ˆj+(b−c)ˆk
Now, PQ.PR=[(b−a)ˆi+(c−b)ˆj+(a−c)ˆk].[(c−a)ˆi+(a−b)ˆj+(b−c)ˆk]
=(b-a)(c-a)+(c-b)(a-b)+(a-c)(b-c)
=a2+b2+c2−ab−bc−ca
|PQ|= √(b−a)2+(c−b)2+(a−c)2
|PR|= √(c−a)2+(a−b)2+(b−c)2
Now, cosθ=PQ.PR|PQ|.|PR|
= a2+b2+c2−ab−bc−ca2a2+2b2+2c2−2ab−2bc−2ca
= a2+b2+c2−ab−bc−ca2(a2+b2+c2−ab−bc−ca)
cosθ=12
∴ θ= π3
Here, ∠QPR=π3