3D Geometry: An angle between the plane, x+y+z=5 and the line of intersection of… | JEE Main 2018

JEE Main 2018 (Online) 15th April Morning ShiftQuestion 1

An angle between the plane, $x+y+z=5$ and the line of intersection of the planes, $3x+4y+z-1=0$ and $5x+8y+2z+14=0$, is

3D Geometry

$\cos^{-1}\left(\frac3{\sqrt{17}}\right)$$\cos^{-1}\left(\sqrt{\frac3{17}}\right)$$\sin^{-1}\left(\frac3{\sqrt{17}}\right)$$\sin^{-1}\left(\sqrt{\frac3{17}}\right)$✓ Correct answer

Solution

Line direction $(3,4,1)\times(5,8,2)=(0,-1,4)\cdot$ scaled; normal $(1,1,1)$. $\sin\theta=\frac{|-1+4|}{\sqrt{17}\sqrt3}=\sqrt{\frac3{17}}$.

3D Geometry - JEE Mathematics question (JEE Main 2018 (Online) 15th April Morning Shift)

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