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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 -16-EXERCISE
  1. Integrate :inttan^-1x/(1+x^2)dx

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  2. Evaluate int0^(pi/2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx

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

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  4. Solve 2y^3(dy)/(dx)=ax

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  5. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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

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

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  8. The angle between the plane 3x+3z-5=0 and the line (x-1)/1=(y-2)/-1=(z...

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  9. Find the equation of the plane passing through the intersection of the...

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  10. Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

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  11. Show that the lines (x-4)/1=(y+3)/-4=(z+1)/7 and (x-1)/2=(y+1)/-3=(z+1...

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  12. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  13. Find the altitude of a right circular cylinder of maximum volume inscr...

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  14. Evaluate the following integrals int(12sinx-2cosx+3)/(sinx+cosx)dx

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  15. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

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  16. Solve the following differential equations (dy)/(dx)+2ytan x= sin x,...

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  17. If A=[[1,1],[-1,-1]], B=[[-1,3],[-3,1]] then show that (A+B)^2 !=A^2 +...

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  18. If f:RrarrR defined by f(x)=5x-8 for all x inR, then show that f is in...

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  19. Prove statement "sin"^(-1) 3/5+ "cos"^(-1)12/13="cos"^(-1) 33/65

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  20. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

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