Let the position vectors of the points $P , Q , R$ and $S$ be $\vec { a } = \hat { i } + 2 \hat { j } - 5 \hat { k } , \vec { b } = 3 \hat { i } + 6 \hat { j } + 3 \hat { k }$, $\vec { c } = \frac { 17 } { 5 } \hat { i } + \frac { 16 } { 5 } \hat { j } + 7 \hat { k }$ and $\vec { d } = 2 \hat { i } + \hat { j } + \hat { k }$, respectively. Then which of the following statements is true? (A) The points $P , Q , R$ and $S$ are NOT coplanar (B) $\frac { \vec { b } + 2 \vec { d } } { 3 }$ is the position vector of a point which divides $P R$ internally in the ratio $5 : 4$ (C) $\frac { \vec { b } + 2 \vec { d } } { 3 }$ is the position vector of a point which divides $P R$ externally in the ratio $5 : 4$ (D) The square of the magnitude of the vector $\vec { b } \times \vec { d }$ is 95
Let the position vectors of the points $P , Q , R$ and $S$ be $\vec { a } = \hat { i } + 2 \hat { j } - 5 \hat { k } , \vec { b } = 3 \hat { i } + 6 \hat { j } + 3 \hat { k }$, $\vec { c } = \frac { 17 } { 5 } \hat { i } + \frac { 16 } { 5 } \hat { j } + 7 \hat { k }$ and $\vec { d } = 2 \hat { i } + \hat { j } + \hat { k }$, respectively. Then which of the following statements is true?
(A) The points $P , Q , R$ and $S$ are NOT coplanar
(B) $\frac { \vec { b } + 2 \vec { d } } { 3 }$ is the position vector of a point which divides $P R$ internally in the ratio $5 : 4$
(C) $\frac { \vec { b } + 2 \vec { d } } { 3 }$ is the position vector of a point which divides $P R$ externally in the ratio $5 : 4$
(D) The square of the magnitude of the vector $\vec { b } \times \vec { d }$ is 95