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Show that the four points with position vectors```4 hat i+8 hat j+12 hat k ,\ 2 hat i+4\ hat j+6 hat k ,3 hat i+5\ hat j+4 hat k\ a n d\ 5 hat i+8\ hat j+5 hat k`are coplanar.

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Show that the four points with position vectors 4hat i+8hat j+12hat k,2hat i+4hat j+6hat k,quad 3hat i+5hat j+4hat k and 5hat i+8hat j+5hat k are coplanar.

Show that the points whose position vectors are 5 hat i+5 hat k ,\ 2 hat i+ hat j+3 hat k\ a n d-4 hat i+3 hat j- hat k are collinear.

Show that the four points having position vectors 6hat i-7hat j,16hat i-19hat j-4hat k,3hat j-6hat k,2hat i+5hat j+10hat k are not coplanar.

Prove that the four points having position vectors are coplanar: 2hat i-hat j+hat k,hat i-3hat j-5hat k and 3hat i-4hat j-4hat k

Show that the four points having position vectors 6hat i-7hat j,16hat i-19hat j-4hat k,3hat j-6hat k,2hat i-5hat j+10k are coplanar.

Show that the points having position vectors 6hat i-7hat j,16hat i-19hat j-4hat k,3hat j-6hat k,2hat i+5hat j+10hat k are not coplanar.

Show that the four points A,B,C and D with position vectors 4hat i+5hat j+hat k,-(hat j+hat k),3hat j+9hat j+4hat k and 4(-hat i+hat j+hat k) respectively are coplanar.

Find the value of lambda for which the four points with position vectors -hat j-hat k,4hat i+5hat j+lambdahat k,3hat i+9hat j+4hat k and 4hat i+4hat j+4hat k are coplanar.

Find the value of lambda for which the four points with position vectors hat j-hat k,4hat i+5hat j+lambdahat k,3hat i+9hat j+4hat k and -4hat i+4hat j+4hat k are coplanar.

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

MOTION-VECTOR -EXERCISE - 3
  1. Find the point R in which the line AB cuts the plane CDE, where positi...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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