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For what value of 'lambda' is the follow...

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

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

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

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

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

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 : 3hati-2hatj+4hatk,6hati+3hatj+2hatk . 5hati+7hatj+3hatk . 2hati+2hatj+5hatk .

MODERN PUBLICATION-VECTORS-Exercise
  1. For what value of 'lambda' is the following vectors coplanar ? veca=ha...

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  2. For what value of 'lambda' are the following vectors coplanar? : hat...

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  3. For what value of 'lambda' is the following vectors coplanar ? veca=2h...

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  4. Using scalar triple product, show that the four points given by positi...

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  5. Find 'x' such that the four points : A(3,2,1),B(4,x,5),C(4,2,-2) and D...

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  6. Show that the four points having position vectors 6hati-7hatj,16hati-1...

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  7. Find the volume of the parallelopiped whose sides are given by the vec...

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  8. Find the volume of the parallelopiped whose sides are given by the vec...

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  9. Let veca=hati+hatj+hatk, vecb=hati and vecc=c1hati+c2hatj+c3hatk. Then...

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  10. Find the volume of the parallelopiped with coteminous edges AB,AC and ...

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  11. Prove that for any two vectors veca and vecb,veca*(vecaxxvecb)=0. Is v...

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  12. If veca,vecb,vecc are perpendicular to each other, prove that [veca....

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  13. What can you conclude about four non-zero vectors veca,vecb,vecc and v...

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  14. Simplify : (vecb+vecc)*{(vecc+veca)xx(veca+vecb)}.

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  15. Prove that {(vecb+vecc)xx(vecc+veca)}.(veca+vecb)=2[veca,vecb,vecc]

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  16. Prove that {(vecb+vecc)xx(vecc+veca)}.(veca+vecb)=2[veca,vecb,vecc]

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  17. Simplify : {(vecb-vecc)xx(vecc-veca)}odot(veca-vecb)

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  18. Simplify : [veca-vecb,vecb-vecc,vecc-veca].

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  19. For any three vectors veca,vecb,vecc show that veca-vecb,vecb-vecc,vec...

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  20. If veca*vecbxxvec=0 and vec(a')=(vecbxxvecc)/(veca*vecbxxvecc), vec(b'...

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