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Show that the four points with position vectors `4hati+8hatj+12hatk,2hati+4hatj+6hatk,3hati+5hatj+4hatk` and `5hati+8hatj+5hatk` are coplanar.

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Find 'lambda' so that the four points with position vectors -hati+3hatj+2hatk,3hati+lambda hatj+4hatk,5hati+7hatj+3hatk and -13hati+17hatj-hatk are coplanar.

Using scalar triple product, show that the four points given by position vectors : 2hati+3hatj+2hatk,4hati-5hatk,3hati+hatj-2hatk and 5hati+3hatj-4hatk are coplanar.

Using scalar triple product, show that the four points given by position vectors 4hati+5hatj+hatk , -hatj-hatk , 3hati+9hatj+4hatk and -4hati+4hatj+4hatk are coplanar.

Using scalar triple product, show that the four points given by position vectors hati+hatj+10hatk , 2hati+3hatj+11hatk , 3hati+2hatj+6hatk and hati-2hatj+4hatk are coplanar.

Show that the four points A,B,C and D with position vectors 4hati+5hatj+hatk,-(hatj+hatk),(3hati+9hatj+4hatk) and 4(-hati+hatj+hatk) respectively are coplanar.

Using scalar triple product prove that the four points whose position vectors are given by the vectors -hatj+hatk , 2hati-hatj-hatk , hati+hatj+hatk and 3hatj+3hatk are coplanar.

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Show that the four points having position vectors 6hati-7hatj,16hati-19hatj-4hatk,3hatj-6hatk,2hati+5hatj+10hatk are not coplanar.

OMEGA PUBLICATION-VECTOR ALGEBRA -MULTIPLE CHOICE QUESTIONS (MCQs)
  1. Show that the four points with position vectors 4hati+8hatj+12hatk,2ha...

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  2. Prove that in any triangle ABC , c = a cos(360-B) + b cos(360-A)

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  3. If veca and vecb are two collinear vectors, then which of the followin...

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  4. If a is a non-zero vector of magnitude V a is a non-zero scalar, then ...

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  5. Let the vectors veca and vecb be such that |veca|=3 and |vecb|=(sqrt2)...

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  6. Area of a rectangle having vertices : A(-hati+1/2 hatj+4hatk),B(hati+1...

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  7. If theta is the angle between two vectors veca and vecb, then veca c...

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  8. Let veca and vecb be two unit vectors and theta is the angle between t...

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  9. If (hati,hatj,hatk) are the usual three perpendicular unit vectors, th...

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  10. Using vectors, find the area of the triangle having vertices A (1, 1, ...

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  11. the angle between vectors veca × vecb and vecb × veca is

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  12. Show that the area of the parallelogram with diagonals veca and vecb, ...

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  13. The area of triangle having adjacent sides veca and vecb is :

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  14. The value of : hati*(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) i...

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  15. If theta is the angle between two vectors veca and vecb, then |veca*ve...

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  16. If veca*vecb=-|veca||vecb|, then theta=

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  17. The projection of the vector veca=2hati+3hatj+2hatk on the vector vecb...

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  18. The product of veca.vecb equals to:

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  19. The product of veca.vecb equals to:

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  20. The vectors a and b are perpendicular, if

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  21. If veca xx vecb=|veca||vecb| sin theta hatn which one is correct

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