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Show that the four points having positio...

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

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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.

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

The point having position vectors 2hati+3hatj+4hatk,3hati+4hatj+2hatk and 4hati+2hatj+3hatk are the vertices of

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.

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.

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

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

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

MODERN PUBLICATION-VECTORS-Exercise
  1. Using scalar triple product, show that the four points given by positi...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If veca*vecb*vecc not= 0 and vec(a')=(vecbxxvecc)/(veca*vecbxxvecc), v...

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  19. If veca*vecbxxvecc= 0 and vec(a')=(vecbxxvecc)/(veca*vecbxxvecc), vec(...

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  20. Represent graphically a displacement of 40 km, 30^o east of north.

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