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The value of lambda for which the plane ...

The value of lambda for which the plane `vecr*(2hati-2hatj+4hatk)=5` is perpendicular to `vecr*(3hati-3hatj+lambdahatk)=7` is :

A

4

B

3

C

-3

D

-4

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Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Find the acute angle between the planes vecr.(hati+2hatj-hatk)=3 and vecr.(2hati-hatj+2hatk)=2 .

For which value of lambda the vector veca = 2hati+hatj-2hatk and vecb = hati-3hatj+lambdahatk are perpendicular to each other :

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Distance between plane defined by 3x + 4y + 5 = 0 and the point (5, 0,...

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  2. Vector equation of the line (x+1)/(2)=(y-4)/(4)=(z+6)/(3)

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  3. The value of lambda for which the plane vecr*(2hati-2hatj+4hatk)=5 is ...

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  4. Direction casines of z-axis are

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  5. If a line has direction ratios <2,-1,-2>, then what are its direction ...

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  6. A line makes angles 45^@ and 60^@ with the positive direction of the a...

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  7. Equation of line passing through the point (2,3,1) and parallel to the...

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  8. If the direction cosines of a vector of magnitude 3 are <2/3, -a/3, 2/...

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  9. Equation of line passing through the point (2,3,1) and parallel to the...

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  10. A unit vector parallel to the straight line: (x-2)/3=(3+y)/-1=(z-2)/-4...

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  11. The angle between a normal to the plane : 2x-y+2z-1=0 and the z axis i...

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  12. Find the coordinates of the Foot of the perpendicular drawn from the ...

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  13. The distance between the x axis and the point (3,12,5) is :

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  14. The shortest distance of the point (a,b,c) from the x-axis is

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  15. Equation of the plane perpendicular to the line x/1=y/2=z/3 and passin...

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  16. The line (x-2)/3=(y-3)/4=(z-4)/5 is parallel to the plane:

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  17. Prove that the angle between any two diagonals of a cube is cos^-1frac...

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  18. The line passing through the points (5, 1, a) and (3, b, 1) crosses th...

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  19. If the straight lines : (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k=(z...

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  20. Let P(3, 2, 6) be a point in space and Q be a point on the line r=(ha...

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