Let O be the origin. Let −−→OP=x^i+y^j−^k and −−→OQ=−^i+2^j+3x^k, x,y∈R,x>0, besuch that ∣∣∣−−→PQ∣∣∣=√20 and the vector −−→OP is perpendicular to −−→OQ. If −−→OR=3^i+z^j−7^k, z∈R is coplanar with −−→OP and −−→OQ, then the value of x2+y2+z2 is equal to :

Let O be the origin. Let −−→OP=x^i+y^j−^k and −−→OQ=−^

1.	Let O be the origin. Let −−→OP=x^i+y^j−^k and −−→OQ=−^i+2^j+3x^k, x,y∈R,x>0, besuch that ∣∣∣−−→PQ∣∣∣=√20 and the vector −−→OP is perpendicular to −−→OQ. If −−→OR=3^i+z^j−7^k, z∈R is coplanar with −−→OP and −−→OQ, then the value of x2+y2+z2 is equal to :
Answer» Let $O$ be the origin. Let $- - \to O P = x^i + y^j -^k$ and $- - \to O Q = -^i + 2^j + 3 x^k, x, y \in R, x > 0,$ be such that $∣ ∣ ∣ - - \to P Q ∣ ∣ ∣ = \sqrt{20}$ and the vector $- - \to O P$ is perpendicular to $- - \to O Q$ . If $- - \to O R = 3^i + z^j - 7^k, z \in R$ is coplanar with $- - \to O P$ and $- - \to O Q,$ then the value of $x^{2} + y^{2} + z^{2}$ is equal to :