The plane 2 x - 2 y + z = 3 is rotated about its line of intersection with the xy - plane by an acute angle α . If the new position of the plane contains the point 3,1 , 1 , then the value of cos ⁡ α is equal to

Question

The plane 2 x - 2 y + z = 3 is rotated about its line of intersection with the xy - plane by an acute angle α . If the new position of the plane contains the point 3,1 , 1 , then the value of cos ⁡ α is equal to, 1 3, 2 3, 7 9, 4 9

MARKS App · Accepted Answer

Let the equation of the plane be 2 x - 2 y + z - 3 + λ z = 0 ∵ it contains the point 3,1 , 1 ⇒6 – 2 + 1 – 3 + λ = 0 ⇒ λ = - 2 Hence, the equation of the plane is 2 x - 2 y - z - 3 = 0 ⇒ cos ⁡ α = 2 2 - 2 - 2 + 1 - 1 4 + 4 + 1 4 + 4 + 1 = 7 9

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