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If theta is the angle between the planes...

If `theta` is the angle between the planes `2x-y+2z=3` and `6x-2y+3z=5`, then `cos theta=?`

A

`11/20`

B

`12/23`

C

`17/25`

D

`20/21`

Text Solution

Verified by Experts

The correct Answer is:
d
Angle between the planes means the angle between their normals.
`costheta=|(2 xx 1)+(-1)xx(-2)+2 xx3|/(sqrt(2^(2)+(-1)^(2)+2^(2))(sqrt(6^(2)+(-2)^(2)+3^(2))=20/(sqrt(9)sqrt(49))=20/(3 xx 7) = 20/21`.
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  6. The angle between the planes 2x-y+z=6 and x+y+2z=7, is

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  8. The equation of a plane through the point (2, 3, 1) and (4, -5, 3) and...

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  9. A variable plane moves so that the sum of the reciprocals of its inter...

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  10. The equation of a plane which is perpendicular to (2hati-3hatj+hatk) a...

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  11. The equation of the plane passing through the point A(2,3,4) and paral...

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  12. The foot of the perpendicular from the point A(7,14,5) to the plane 2x...

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  13. The equation of the plane which makes with coordinate axes, a triangle...

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  14. The intercepts made by the plane vecr.(2hati-3hatj+4hatk)=12 are

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  15. The angle between the line (x-2)/1=(y+3)/-2=(z+4)/-3 and the plane 2x-...

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  16. The angle between the line vecr=(hati+hatj-3hatk)+lambda(2hati+2hatj+h...

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  17. Find the distance of the point (1,2,5) from the plane vecr.(hati+hatj+...

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  18. The distance between the parallel planes 2x-3y+6z=5 and 6x-9y+18z+20=0...

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  19. The distance between the planes x+2y-2z+1=0 and 2x+4y-4z+5=0, is

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  20. The image of the point (1, 3, 4) in the plane 2x-y+z+3=0 is (3,\ 5,\ 2...

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