jee-main 2025 Q8

jee-main · India · session1_23jan_shift2 Vectors Introduction & 2D Section Ratios and Intersection via Vectors
Let the point A divide the line segment joining the points $P ( - 1 , - 1,2 )$ and $Q ( 5,5,10 )$ internally in the ratio $\mathrm { r } : 1 ( \mathrm { r } > 0 )$. If O is the origin and $( \overrightarrow { \mathrm { OQ } } \cdot \overrightarrow { \mathrm { OA } } ) - \frac { 1 } { 5 } | \overrightarrow { \mathrm { OP } } \times \overrightarrow { \mathrm { OA } } | ^ { 2 } = 10$, then the value of r is :
(1) $\sqrt { 7 }$
(2) 14
(3) 3
(4) 7
Let the point A divide the line segment joining the points $P ( - 1 , - 1,2 )$ and $Q ( 5,5,10 )$ internally in the ratio $\mathrm { r } : 1 ( \mathrm { r } > 0 )$. If O is the origin and $( \overrightarrow { \mathrm { OQ } } \cdot \overrightarrow { \mathrm { OA } } ) - \frac { 1 } { 5 } | \overrightarrow { \mathrm { OP } } \times \overrightarrow { \mathrm { OA } } | ^ { 2 } = 10$, then the value of r is :\\
(1) $\sqrt { 7 }$\\
(2) 14\\
(3) 3\\
(4) 7