The plane 2 x -2 y - z -3 is rotated about the line where it cuts the xy - plane by an acute angle - If the new position of plane contains the point 3-1-1 then 9 cos- is equal to

nbsp; Equation of new plane will be 2x 2y+z 3+λ z=0 Point (3,1,1) lie on it nbsp; ⇒λ= 2 Equation of new plane: 2x 2y z=3 cosα=4+4 13×3=7/9 ...

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Standard XII

Mathematics

Direction Ratios

The plane 2 x...

Question

The plane $2 x - 2 y + z = 3$ is rotated about the line where it cuts the $x y -$ plane by an acute angle $α$ . If the new position of plane contains the point $(3, 1, 1)$ then $9 cos α$ is equal to

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Solution

Equation of new plane will be $2 x - 2 y + z - 3 + λ z = 0$
Point $(3, 1, 1)$ lie on it
$\Rightarrow λ = - 2$
Equation of new plane: $2 x - 2 y - z = 3$
$cos α = \frac{4 + 4 - 1}{3 \times 3} = \frac{7}{9}$

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The plane 2x−2y+z=3 is rotated about the line where it cuts the xy−plane by an acute angle α. If the new position of plane contains the point (3,1,1) then 9cosα is equal to

Equation of new plane will be 2x−2y+z−3+λz=0 Point (3,1,1) lie on it ⇒λ=−2 Equation of new plane: 2x−2y−z=3 cosα=4+4−13×3=79

The plane $2 x - 2 y + z = 3$ is rotated about the line where it cuts the $x y -$ plane by an acute angle $α$ . If the new position of plane contains the point $(3, 1, 1)$ then $9 cos α$ is equal to

Equation of new plane will be $2 x - 2 y + z - 3 + λ z = 0$
Point $(3, 1, 1)$ lie on it
$\Rightarrow λ = - 2$
Equation of new plane: $2 x - 2 y - z = 3$
$cos α = \frac{4 + 4 - 1}{3 \times 3} = \frac{7}{9}$