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Show that the points A(2hati-hatj+hatk),...

Show that the points `A(2hati-hatj+hatk),B(hati-3hatj-5hatk) and C(3hati-4hatj-4hatk)` are the vertices of right angled triangle.

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Show that the points A(2hati-hatj+hatk),B(hati-3hatj-5hatk),C(3hati-4j-4hatk) are vertices of a right angled triangle.

Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7hati-hatk) are collinear.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Show that the points A,B and C having position vectors (3hati - 4hatj - 4hatk), (2hati - hatj + hatk) and (hati - 3hatj - 5hatk) respectively, from the vertices of a right-angled triangle.

Show that the vectors hati-3hatj+2hatk,2hati-4hatj-hatk and 3hati+2hatj-hatk and linearly independent.

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

The vectors 2 hati - ahtj + hatk, hati -3 hatj - 5 hatj and sqrt3 hati - 4 hatj - 4 hatk are the sides of a triange, which is :

Show that the points A,B and C with position vectors , veca=3hati-4hatj-4hatk,vecb=2hati-hatj+hatkandvecc=hati-3hatj=5hatk ,respectively form the vertices of a right angled triangle.

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

If the vectors 6hati-2hatj+3hatk, 2hati+3hatj-6hatk and 3hati+6hatj-2hatk form a triangle, then it is

SUNSTAR PUBLICATION-P.U BOARD LATEST MODEL QUESTION PAPER - 3 -PART-C
  1. If x=a(costheta+logtan(theta/2)) and y=a sin theta," show that "(dy)/(...

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  2. At what points, the function f(x)=sinx-cosx,0ltxlt2pi, attains local m...

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  3. Evaluate int" e"^(x)sinx dx

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  4. Find int(sinx)/(sin(x-a))dx

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  5. Find the area of the region enclosed by the circle x^(2)+y^(2)=a^(2) b...

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  6. Solve (2dy)/(dx)=(y)/(x)+(y^(2))/(x^(2)))

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  7. Show that the points A(2hati-hatj+hatk),B(hati-3hatj-5hatk) and C(3hat...

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  8. Three vectors satisfy the condition veca,vecb and vecc satisfy the con...

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

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  10. A random variable x has the following probability distribution. D...

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  11. If f:RrarrR defined by f(x)=(4x+3), show that f is invertible and find...

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  12. If A=[(-1,2),(2,3)],B=[(1,-3),(-3,4)] verify that AB-BA is a skew symm...

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  13. If A=[(2,-3,5),(3,2,-4),(1,1,-2)], find A^(-1). Using A^(-1) solve th...

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  14. If y=e^(a cos^(-1)x),-2lexle1, show that (1-x^(2))(d^(2)y)/(dx^(2))-xd...

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  15. Sand is pouring from a pipe at the rate of 12cm^(3)//sec. The falling ...

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  16. Find the integral of 1/(sqrt(x^(2)-a^(2))) with respect to x and evalu...

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  17. Find the area bounded by the curve x^(2)=4y and the line x=4y-2.

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  18. Derive the equation of a plane in normal form both in the vector and C...

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  19. Solve dy/dx+(2xy)/(1+x^(2))=(4x^(2))/(1+x^(2))

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  20. The probability that a bulb produced by a factory will fuse after 150 ...

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