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If the position vectors of the points A, B, C are `2hat(i) + hat(j) - hat(k), 3hat(i) - 2hat(j) + hat(k)` and `hat(i) + 4hat(j) - 3hat(k)` respectively, then prove that A, B, C are collinear.

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The position vectors of the point A,B,C and D are 4hat(i)+3hat(j)-hat(k),5hat(i)+2hat(j)+2hat(k),2hat(i)-2hat(j)-3hat(k) and 4hat(i)-4hat(j)+3hat(k) , respectively. Show that vec(AB) and vec(CD) are parallel.

Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

Show that the following vectors are coplanar. hat(i) - 2hat(j) + 2hat(k), 3hat(i) + 4hat(j) + 5hat(k), -2hat(i) + 4hat(j) - 4hat(k)

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

Show that the following vectors are coplanar. hat(i) + 2hat(j) + 3hat(k), -2hat(i) - 4hat(j) + 5hat(k), 3hat(i) + 6hat(j) + hat(k)

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  2. Determine the area of the parallelogram whose sides are the vectors 2h...

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  3. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  4. Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...

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  5. Find the value of lambda such that the following vectors are coplanar:...

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  6. Prove that four points with position vectors hati+hatj-3hatk, 2hati -h...

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  7. Using vector method find the area of the triangle with vertices (1, 0,...

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  8. Write the volume of the parallelopiped whose sides are given by-hatj, ...

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  9. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  10. Write a vector normal to hati+hatk and hati+hatj.

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  11. If vec a = (2,-2,1), vec b = (2,3,6) and vec c = (-1,0,2),Find the mag...

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  12. Find the angle between the vectors 3hati+ 4hatj and2hati+hatj+hatk.

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  13. Find the unit vector in the direction of veca-vecb where veca= 4hati +...

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  14. If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-v...

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  15. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

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  16. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

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  17. Prove that the four points with position vectors 2veca+3vecb-vecc, vec...

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  18. Show that veca, vecb and vec c are coplanarif veca+vecb,vecb+vecc and ...

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  19. Find the vector vecp which is perpendicular to both vecalpha = 4hati +...

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  20. If veca=hati+hatj+hatk and vecb=hati-hatk . Find a vector vecc such th...

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