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The position vectors of the angular poin...

The position vectors of the angular points of a tetrahedron are `A(3 hat i-2 hat j+hat k),B(3 hat i+hat j+5 hat k),C(4 hat i+3 hat k)` and `D(hat i)` Then the acute angle between the lateral face ADC and the base face ABC is:

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The correct Answer is:
`cos theta = (2)/(sqrt(89)sqrt(41))`
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The position vectors of the angular points of a tetrahedron are A(3hat i-2hat j+hat k),B(3hat i+hat j+5hat k),C(4hat i+3hat k) and D(hat i) Then the acute angle between the lateral face ADC and the base face ABC is:

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

The angle between the vectors (hat i + hat j + hat k) and ( hat i - hat j -hat k) is

Determine the sine of the angle between the vectors ( 3 hat i+ 3hat j+ 4 hat k) and ( 3 hat i-2 hat j - 4 hat k0 .

Find the angle between the vectors hat i-2hat j+3hat k and 3hat i-2hat j+hat k

Find the sine of the angle between the vectors vec A = 3 hat i - 4 hat j + 5 hat k and vec B = hat i - hat j + hat k .

the angle between the vectors 2hat i-3hat j+2hat k and hat i+5hat j+5hat k is

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

If the vectors 3 hat i +3 hat j +9 hat k and hat i +a hat j +3 hat k are parallel, then a =

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection

MOTION-VECTOR -EXERCISE - 3
  1. Find vector vec(v) which is coplanar with the vectors hat(i) + hat(j...

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  2. Find the point R in which the line AB cuts the plane CDE, where positi...

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  3. The position vectors of the angular points of a tetrahedron are A(3 ha...

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  4. Show that the four points with position vectors4 hat i+8 hat j+12 hat ...

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  5. Examine for coplanarity of the following sets of points 3vec(a) + 2...

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  6. The length of the edge of the regular tetrahedron DABC is 'a'. Point E...

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  7. The position vectors of the four angular points of a tetrahedron ar...

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  8. The position vectors of the four angular points of a tetrahedron ar...

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  9. The position vectors of the four angular points of a tetrahedron ar...

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  10. The position vectors of the four angular points of a tetrahedron ar...

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  11. ABCD is a tetrahedron with pv's of its angular point as A(-5, 22, 5); ...

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  12. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

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  13. Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) ...

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  14. Are the following set of vectors linearly independent? vec(a) = h...

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  15. Are the following set of vectors linearly independent? vec(a) = - 2...

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  16. the resultant of two vectors vec(a) & vec(b) is perpendicular to ve...

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  17. Given three points on the xy plane on O(0, 0), A(1, 0) and B(–1, 0). P...

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  18. Vector vec O A= hat i+2 hat j+2 hat k turns through a right angle ...

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  19. If p vec x +( vec x xx vec a )= vec b ;(p!=0) prove that & vecx...

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  20. Given two orthogonal vectors vec(A) and vec(B) each of length unity ...

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