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Show that the four points with position vectors `4hati+8hatj+12hatk,2hati+4hatj+6hatk,3hati+5hatj+4hatk` and `5hati+8hatj+5hatk` are coplanar.

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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.

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 4hati+5hatj+hatk , -hatj-hatk , 3hati+9hatj+4hatk and -4hati+4hatj+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.

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.

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

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

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

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

Show that the four points having position vectors 6hati-7hatj,16hati-19hatj-4hatk,3hatj-6hatk,2hati+5hatj+10hatk are not coplanar.

OMEGA PUBLICATION-HP BOARD MARCH 2017-SERIES -C
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  2. Solve the differential equation (dy)/(dx)=(x+1)/(2-y),(y!=2)

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  3. Show that the four points with position vectors 4hati+8hatj+12hatk,2ha...

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  4. Find the angle between the pair of lines (x-5)/7=(y+2)/(-5)=z/1 and x...

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  9. Find the equations of the tangent and normal to the hyperbola x^2/a^2 ...

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  11. Find the area of region bounded by The parabola y^(2)=4ax and its la...

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  12. Area lying between the curve y^2 = 4x and the line y = 2x is :

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  13. Find the shortest distance between the lines vecr=hati+2hatj+3hatk+lam...

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  14. Find the coordinates of the points where the line through (5,1,6) and ...

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  15. Solve the following linear programming problem graphically : Maximize ...

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

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

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  18. The drivateive of tan45^(@) is

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

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