Q13 of 230 Page 30

Find the angle between the line and the plane 3x + 4y + z + 5 = 0.

We know that line is parallel to plane a2x + b2y + c2z + d2 = 0 if a1a2 + b1b2 + c1c2 = 0 is given by

……(1)


Now, given equation of line is



So, a1 = 3 , b1 = – 1 and c1 = 2


Equation of plane is 3x + 4y + z + 5 = 0


So, a2 = 3, b2 = 4, c2 = 1 and d2 = – 5


∴


⇒


⇒


⇒ sinθ = ⇒ θ = sin – 1(


∴ the angle between the plane and the line is sin – 1(


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