jee-main 2018 Q89

jee-main · India · 15apr_shift1 Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines

An angle between the plane, $x + y + z = 5$ and the line of intersection of the planes, $3 x + 4 y + z - 1 = 0$ and $5 x + 8 y + 2 z + 14 = 0$, is
(1) $\cos ^ { - 1 } \left( \frac { 3 } { \sqrt { 17 } } \right)$
(2) $\cos ^ { - 1 } \left( \sqrt { \frac { 3 } { 17 } } \right)$
(3) $\sin ^ { - 1 } \left( \frac { 3 } { \sqrt { 17 } } \right)$
(4) $\sin ^ { - 1 } \left( \sqrt { \frac { 3 } { 17 } } \right)$

An angle between the plane, $x + y + z = 5$ and the line of intersection of the planes, $3 x + 4 y + z - 1 = 0$ and $5 x + 8 y + 2 z + 14 = 0$, is\\
(1) $\cos ^ { - 1 } \left( \frac { 3 } { \sqrt { 17 } } \right)$\\
(2) $\cos ^ { - 1 } \left( \sqrt { \frac { 3 } { 17 } } \right)$\\
(3) $\sin ^ { - 1 } \left( \frac { 3 } { \sqrt { 17 } } \right)$\\
(4) $\sin ^ { - 1 } \left( \sqrt { \frac { 3 } { 17 } } \right)$

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