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If the position vectors of the points A,...

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-MODEL QUESTION PAPER 13-EXERCISE
  1. If x=asec theta, y=b tan theta, then prove that (d^(2)y)/(dx^(2))=-(b^...

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  2. Find the points on the curve x^(2) + y^(2) - 2x - 3 = 0 at which the t...

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  3. For which value of x, the function f(x)=4-x-x^2is maximum or minimum.

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  4. Evaluate int (x+3)^2dx

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  5. Evaluateint0^pi (2/4)sinsqrtxdx

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  6. Evaluate int sin^-1 x dx

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  7. Find the area bounded by the line y = 2x, x- axis and the ordinate x =...

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  8. Solve(dy)/(dt)=e^(3t+5y)

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

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  10. If veca = (2,-2,1), vecb = (2,3,6) and vecc = (-1,0,2), Find the magni...

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  11. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  12. Find the equation of the plane passing through (3,-6,-9) and parallel ...

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  13. If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...

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  14. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  15. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

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  16. Evaluate int0^(pi//2) (cos x)/ ((2+ sin x)(3+sin x))dx

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  17. Find the area of the region between the curves y=cos x" and "y=sinx,x ...

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  18. Solve (x-y+1)dx-(x+y+5)dy=0

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  19. Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+...

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  20. Find the equation of the plane through the points (2, 2,1)and (9, 3, 6...

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