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The angle theta between the line vecr=ve...

The angle `theta` between the line `vecr=veca+lambdavecb` and the plane `vecr.hatn=d` is given by

A

`vecb.vecn=0,veca.vecn=q`

B

`vecb.vecn" "ne0,veca.vecn" "ne q`

C

`vecb.vecn=0,veca.vecn" "ne q`

D

`vecb.vecn" "ne0,veca.vecn" "ne q`

Text Solution

Verified by Experts

The correct Answer is:
c
we must have `vecb.vecn=0` (because the line and the plane must be parallel) and `veca.vecn""neq` (as point `veca` on the line should not lie on the plane).
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
  1. Distance of point P(vecP) from the plane vecr.vecn=0 is

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  2. The reflection of the point veca in the plane vecr.vecn=q is (A) veca+...

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  3. The angle theta between the line vecr=veca+lambdavecb and the plane ve...

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  4. If a line makes an angel of pi/4 with the positive direction of eac...

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  5. The ratio in which the plane vec rdot( vec i-2 vec j+3 vec k)=17 d...

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  6. then image of the point (-1,3,4) in the plane x-2y=0

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  7. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

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  8. Let L be the line of intersection of the planes 2x+3y+z=1a n dx+3y+2z=...

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  9. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

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  10. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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  11. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=...

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  12. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

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  13. A line makes an angel theta with each of the x-and z-axes. If the a...

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  14. The shortest distance from the plane 12 x+y+3z=327 to the sphere x^...

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  15. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  16. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4...

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  17. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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  18. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  19. Two systems of rectangular axes have the same origin. If a plane cu...

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  20. Find the equation of a plane which passes through the point (3, 2, 0...

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