Q77. Let three vectors $\overrightarrow { \mathrm { a } } = \alpha \hat { i } + 4 \hat { j } + 2 \hat { k } , \overrightarrow { \mathrm {~b} } = 5 \hat { i } + 3 \hat { j } + 4 \hat { k } , \overrightarrow { \mathrm { c } } = x \hat { i } + y \hat { j } + z \hat { k }$ form a triangle such that $\vec { c } = \vec { a } - \vec { b }$ and the area of the triangle is $5 \sqrt { 6 }$. If $\alpha$ is a positive real number, then $| \vec { c } | ^ { 2 }$ is equal to: (1) 16 (2) 14 (3) 12 (4) 10
Q77. Let three vectors $\overrightarrow { \mathrm { a } } = \alpha \hat { i } + 4 \hat { j } + 2 \hat { k } , \overrightarrow { \mathrm {~b} } = 5 \hat { i } + 3 \hat { j } + 4 \hat { k } , \overrightarrow { \mathrm { c } } = x \hat { i } + y \hat { j } + z \hat { k }$ form a triangle such that $\vec { c } = \vec { a } - \vec { b }$ and the area of the triangle is $5 \sqrt { 6 }$. If $\alpha$ is a positive real number, then $| \vec { c } | ^ { 2 }$ is equal to:\\
(1) 16\\
(2) 14\\
(3) 12\\
(4) 10