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The line barr = 2bari - 3barj - bark + l...

The line `barr = 2bari - 3barj - bark + lambda (bari - barj + 2bark)` lies in the plane `barr .(3bari+barj-bark)+2=0`.

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Show that the points bari-barj+3bark and 3(bari +barj+bark) are equidistant from the plane barr.(5bari+2barj-7bark)+9=0 and lies on opposite side of it.

The cartesian equation of the plane barr.(bari+barj-bark)=2 is..........

Find the angle between the lines barr=3bari-2barj+6bark+lambda(2bari+barj+2bark) and barr=(2barj-5bark)+mu(6bari+3barj+2bark). Hint for solution : Angle between line barr=a_1+lambda barb_1 and r=bara_2+mubarb_2 then angle between them is obtained from cos theta=(|b_1.b_2|)/(|b_1|.|b_2|) .

The angle between the line vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+hatk) and the plane barr.(3hati-4hatj-hatk)+5=0 is sin^(-1)((5)/(2sqrt(91))) .

The vector equation of the plane containing the line vec r (-2 hat i - 3 hat + 4 hatk) + lambda (3 hat i - 2 hat j - hat k) and the point hat i + 2 hatj + 3 hat k is ..........

If the foot of perpendicular drawn from the origin to a plane is (5, - 3, - 2), then the equation of plane is barr.(5bari-3barj-2bark)=38 .

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

vec(AB)=3bari-barj+bark and vec(CD)= -3bari+2barj+4bark are two vectors. The position vectors of the points A and C are 6bari + 7barj + 4bark and -9bari + 2bark respectively. Find the position vector of a point P on the line AB and a point Q on the line CD such that vec(PQ) is perpendicular to vec(AB) and vec(CD) both.

The point (-2, -3, -4) lies in the _____

Find the equation of the plane through the intersection of the planes vecr.(bari+3barj)-6=0 and barr.(3bari-barj-4bark)=0 , whose perpendicular distance from origin is unity.

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-SOLUTION OF NCERT EXAMPLAR PROBLEMS (Short Answer Type Question)
  1. If the directions cosines of a line are k, k and k then ..........

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  2. The distance of the plane barr.(2/7i+3/7j-6/7k)=1 from the origin is …...

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  3. The sine of the angle between the straight line (x-2)/(3)=(y-3)/(4)=(z...

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  4. The reflection of the point (alpha,beta,gamma) in the xy - plane is .....

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  5. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4...

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  6. The locus represented by xy + yz = 0 is .........

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  7. The plane 2x – 3y + 6z - 11 = 0 makes an angle sin^(-1)alpha with X- a...

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  8. A plane passes through the points (2, 0, 0) (0,3,0) and (0, 0, 4). The...

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  9. The direction cosines of the vector 2bari + 2barj - bark are ............

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  10. The cartesian equation of a line is (x-5)/(3)=(y+4)/(7)=(z-6)/(2).Writ...

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  11. The vector equation of the line through the points (3, 4, -7) and (1, ...

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  12. The cartesian equation of the plane barr.(bari+barj-bark)=2 is...........

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  13. The unit vector normal to the plane x + 2y + 3z - 6 = 0 is (1)/(sqrt(1...

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  14. The intercepts made by the plane 2x - 3y + 5z + 4 = 0 on the co-ordina...

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  15. The angle between the line vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+h...

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  16. The angle between the planes barr.(2bari-3barj+bark)=1 and barr.(i-j)=...

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  17. The line barr = 2bari - 3barj - bark + lambda (bari - barj + 2bark) li...

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  18. The cartesian equation of a line is (x-5)/(3)=(y+4)/(7)=(z-6)/(2).Writ...

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  19. The equation of a line, which is parallel to 2bari + barj + 3bark and ...

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  20. If the foot of perpendicular drawn from the origin to a plane is (5, -...

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