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Show that the point 2 hat i ,- hat i-...

Show that the point `2 hat i ,- hat i-4 hat j` and `- hat i+4 hat j` from an isosceles triangle.

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Show that the vectors 2 hat i-3 hat j+4 hat k and -4 hat i+6 hat j-8 hat k are collinear.

Show that the vectors 2 hat i-3 hat j+4 hat k\ a n d-4 hat i+6 hat j-8 hat k are collinear.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are collinear, then

Show that the points hat i- hat j+3 hat ka n d3( hat i+ hat j+ hat k) are equidistant from the plane vec rdot(5 hat i+2 hat j+ hat k)+9=0 and lie on opposite sides of it.

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

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

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

Write the value of [ hat i+ hat j\ hat j+ hat k\ hat k+ hat i]

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. A B C D is parallelogram and P is the point of intersection of its dia...

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  2. If O is a point in space, A B C is a triangle and D , E , F are ...

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  3. Show that the point 2 hat i ,- hat i-4 hat j and - hat i+4 hat j fr...

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  4. If vec a be the position vector whose tip is (5,-3), find the c...

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  5. Show that the line segments joining the mid-points of opposite side...

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  6. A B C D are four points in a plane and Q is the point of interse...

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  7. If vec aa n d vec b are non-collinear vectors, find the value of x fo...

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  8. The projection of a vector on the coordinate axes are (6,-3,2) Find ...

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  9. If vec a , vec b, vec c are three non- null vectors such that any tw...

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  10. Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n...

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  11. Show that the points A ,B ,C with position vectors -2 vec a+3 vec b+5 ...

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  12. Prove that the line joining the mid-points of the diagonals of a trape...

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  13. Prove that the segment joining the middle points of two non-paralle...

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  14. Using vector method, prove that the line segments joining the mid-p...

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  15. If the points with position vectors 60 hat i+2 hat j , 40 hat i-8 hat ...

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  16. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

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  17. If D and E are the mid-points of sides AB and AC of a triangle A B C r...

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  18. If G is the centroid of a triangle A B C , prove that vec G A+ vec G ...

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  19. Prove using vectors: Medians of a triangle are concurrent.

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  20. Points L, M, N divide the sides BC, CA, AB of ABC in the ratio 1:4, 3:...

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