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Show that the following vectors are copl...

Show that the following vectors are coplanar : `3hati-2hatj+4hatk,6hati+3hatj+2hatk`. `5hati+7hatj+3hatk`. `2hati+2hatj+5hatk`.

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Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3hatj-5hatk,3hati-4hatj-4hatk .

Show that the following vectors are coplanar : hati-hatj+hatk,6hati-hatk and 4hati+2hatj-3hatk .

Show that the following vectors are collinear : 2hati-3hatj+4hatk and -4hati+6hatj-8hatk .

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

Show that the following vectors are coplanar : veca=hati-2hatj+3hatk,vecb=-2hati+3hatj-4hatk and vecc=hati-3hatj+5hatk .

For what value of 'lambda' is the following vectors coplanar ? veca=2hati-4hatj+5hatk,hati-lambda hatj+hatk and 3hati+2hatj-5hatk .

Show that the vectors veca=hati-2hatj+3hatk,vecb=-2hati+3hatj-4hatk and vecc=hati-3hatj+5hatk are coplanar.

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

MODERN PUBLICATION-VECTORS-Exercise
  1. If veca=-2hati+3hatj+5hatk,vecb=hati+2hatj+3hatkandvecc=7hati-hatk are...

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  2. Show that the following vectors are coplanar : hati-hatj+hatk,6hati-ha...

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  3. Show that the following vectors are coplanar : 3hati-2hatj+4hatk,6hati...

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  4. Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3h...

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  5. Show that the points A(3,-2,1),B(1,-3,5),C(2,1,-4) do not form a right...

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  6. If the position vectors of the vertices of a triangle are : vecA=hati+...

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  7. If veca = hati + hatj+hatk, vecb = 2hati-hatj+3hatk and vecc = hati-2h...

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  8. Show that the four points A,B,C,D with position vectors veca*vecb*vecc...

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  9. Show that the four points P,Q,R,S with position vectors vecp,vecq,vecr...

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  10. Prove that the necessary and sufficient condition for three vectors ve...

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  11. If veca,vecb,vecc,vecd respectively, are position vectors representing...

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  12. If Q is the point of intersection of the medians of a triangle ABC, pr...

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  13. G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(G...

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  14. Let veca,vecb,vecc,vecd be the position vectors of the four distinct p...

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  15. Show that the line joining any vertex of a parallelogram to the mid-po...

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  16. Prove that the figure formed by joining the mid-points of the pairs of...

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  17. Show that if P,A,B are any three points, then lambda vec(PA)+mu vec(PB...

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  18. Obtain the dot product of the vectors : veca=veci-hatj+hatk and vecb=v...

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  19. Write the magnitude of a vector veca in terms of dot product.

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  20. If veca=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk find the projectio...

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