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Show that the four points A,B,C and D wi...

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.

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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.

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 : 2hati+3hatj+2hatk,4hati-5hatk,3hati+hatj-2hatk and 5hati+3hatj-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 position vectors of A,B,C are 2hati+hatj-hatk,3hati-2hatj+hatk and hati+4hatj-3hatk respectively. Show that A, B and C are collinear.

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.

Area of a rectangle having vertices A, B, C and D with position vectors : -hati + (1/2)hatj + 4hatk, hati + (1/2)hatj + 4hatk, hati - (1/2)hatj + 4hatk and -hati - (1/2)hatj + 4hatk , respectively is:

Show that the three points with position vectors -2hati+3hatj+5hatk , hati+2hatj+3hatk and 7hati-hatk are collinear.

Using scalar triple product prove that the four points whose position vectors are given by the vectors , hati-hatj+hatk , 2hati-2hatj , 3hati+2hatj+2hatk and 4hati+hatj+hatk are coplanar.

OMEGA PUBLICATION-HP BOARD MARCH 2017-SERIES -C
  1. Show that the four points A,B,C and D with position vectors 4hati+5hat...

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  2. The principal value of cos^(-1)(1/sqrt 2) is ............. .

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  3. If A and B are symmetric matrices of same order then AB - BA is a :

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  4. The drivateive of tan45^(@) is

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  5. Find the approximate change in the volume V of a cube of side x metres...

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  6. An antiderivative of sin mx is

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  7. The degree of the differential equation (d^(3)y)/(dx^(3))+2((d^(2)y)/(...

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  8. Find the projection of the vector hati+3hatj+7hatk on the vector 7hati...

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  9. The dot product of the two vectors veca and vecb is

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  10. The distance of the plane 2x-y+2z+3=0 from the point (3,2,1) is

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  11. If A and b are any two events such that P(A)+P(B)-P(A "and"B)=P(A), t...

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  12. By using elementary transformation find the inverse of the matrix : A ...

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  13. Find the values of x and y from the equation 2[(x,5),(y,-3)]+[(3,-4),(...

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  14. Find the values of k so that the function f, defined by f(x)={(kx+1,"i...

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  15. Find the intervals in which the function f given by f(x)=4x^(3)-6x^(2)...

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  16. Form a differential equation representing the family of curves y^(2) =...

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  17. Let T be the set of all triangles in a plane with R a relation in T gi...

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  18. Prove that cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)=sin^(-1)""(56)/(65)

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  19. Write tan^(-1)((sqrt(1+x^(2))-1)/(x)),xne0 simplest form.

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  20. Using the properties of determinants, show that |(1+a,1,1),(1,1+b,1),(...

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  21. Find (dy)/(dx) if xy^2 + y^2 = tan x + y

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