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If the lines vec r = vec a + lambda (vec...

If the lines `vec r = vec a + lambda (vec b xx vec c)` and `vec r = vec b + mu (vec c xx vec a)` are intersect then ...............

A

`vec a xx vec c = vec b xx vec c`

B

`vec a. vec c = vec b . vec c `

C

`vec b xx vec a = vec c xx vec a`

D

None of these

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B
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Let vec(X),vec(Y) and vec(Z) be three vectors such that |vec(X)|=|vec(Y)|=|vec(Z)|=sqrt(2) . The angle between vec(X),vec(Y) and vec(Z) with each other 60^(@) . vec(X)xx(vec(Y)xx vec(Z))=vec(a),vec(Y)xx(vec(Z)xx vec(X))=vec(b) and vec(X)xx vec(Y)=vec( C ) Vector vec(Y) = ............... .

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MULTIPLE CHOICE QUESTIONS (MCQs)
  1. The equation of the plane passing through origin and the line of inter...

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  2. The equation of the plane containing the lines vec r = vec (a1) + lamb...

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  3. If the lines vec r = vec a + lambda (vec b xx vec c) and vec r = vec b...

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  4. The distance between the planes 2x + 2y-z + 2 = 0 and 4x + 4y -2x +...

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  5. The plane 2x - (1- lambda) y+ 3 lambda z= 0 is passing through the lin...

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  6. A plane passes through (1,1,1). It is perpendicular to the line (x-1)/...

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  7. The equation of the plane passing through the line of intersection of ...

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  8. The vector equation of the plane containing the line vec r (-2 hat i -...

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  9. The plane passing through the intersection of the planes x+y +z =1 and...

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  10. The equation of line passing through the point (-4,3,1) parallel to th...

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  11. The equation of plane containing the line x/2 = y/3 = z/4 and perpendi...

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  12. If the lines x = ay + b ,z = cy + d and x= a'z + b',y = c'z + d'' are ...

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  13. The plane parallel to the lines (x+2)/(3) = (y-2)/(-1) = (z+1)/(2) an...

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  14. A point A is on the line vec r = (1- 3mu ) hat i + (mu - 1) hat j + ...

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  15. The distance of the point (2,-1,-2) from the line (x-1)/(2) = (y+3)/(2...

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  16. Three planes 4y+6z = 5, 2x + 3y + 5z = 5 and 6x + 5y + 9z = 10 ..........

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  17. A variable plane makes with the co-ordinates plane, tetrahedron of con...

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  18. If the lines (2x-5)/(k) = (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)/(2) ...

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  19. If the plane 2x + 3y + 4z = 1 intersects X-axis, Y-axis and Z-axis at...

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  20. Distance between the two planes 2x-2y+z = 5 and 6x-6y+3z = 25 is ........

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