jee-main 2020 Q69

jee-main · India · session2_05sep_shift1 Vector Product and Surfaces
If the volume of a parallelopiped, whose coterminous edges are given by the vectors $\overrightarrow { \mathrm { a } } = \hat { i } + \hat { j } + n \widehat { k }$, $\overrightarrow { \mathrm { b } } = 2 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } - n \hat { k }$ and, $\overrightarrow { \mathrm { c } } = \hat { \mathrm { i } } + n \hat { j } + 3 \hat { k } ( \mathrm { n } \geq 0 )$ is 158 cubic units, then :
(1) $\overrightarrow { \mathrm { a } } \cdot \overrightarrow { \mathrm { c } } = 17$
(2) $\overrightarrow { \mathrm { b } } \cdot \overrightarrow { \mathrm { c } } = 10$
(3) $n = 7$
(4) $n = 9$
If the volume of a parallelopiped, whose coterminous edges are given by the vectors $\overrightarrow { \mathrm { a } } = \hat { i } + \hat { j } + n \widehat { k }$, $\overrightarrow { \mathrm { b } } = 2 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } - n \hat { k }$ and, $\overrightarrow { \mathrm { c } } = \hat { \mathrm { i } } + n \hat { j } + 3 \hat { k } ( \mathrm { n } \geq 0 )$ is 158 cubic units, then :\\
(1) $\overrightarrow { \mathrm { a } } \cdot \overrightarrow { \mathrm { c } } = 17$\\
(2) $\overrightarrow { \mathrm { b } } \cdot \overrightarrow { \mathrm { c } } = 10$\\
(3) $n = 7$\\
(4) $n = 9$