jee-main 2023 Q76

jee-main · India · session2_15apr_shift1 Vectors 3D & Lines Vector Algebra and Triple Product Computation
Let $S$ be the set of all $( \lambda , \mu )$ for which the vectors $\lambda \hat { i } - \hat { j } + \widehat { k } , \hat { i } + 2 \hat { j } + \mu \widehat { k }$ and $3 \hat { i } - 4 \hat { j } + 5 \widehat { k }$, where $\lambda - \mu = 5$, are coplanar, then $\sum _ { ( \lambda , \mu ) \in S } 80 \left( \lambda ^ { 2 } + \mu ^ { 2 } \right)$ is equal to
(1) 2210
(2) 2130
(3) 2290
(4) 2370
Let $S$ be the set of all $( \lambda , \mu )$ for which the vectors $\lambda \hat { i } - \hat { j } + \widehat { k } , \hat { i } + 2 \hat { j } + \mu \widehat { k }$ and $3 \hat { i } - 4 \hat { j } + 5 \widehat { k }$, where $\lambda - \mu = 5$, are coplanar, then $\sum _ { ( \lambda , \mu ) \in S } 80 \left( \lambda ^ { 2 } + \mu ^ { 2 } \right)$ is equal to\\
(1) 2210\\
(2) 2130\\
(3) 2290\\
(4) 2370