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The position vectors of the points `A ,\ B ,\ C` are `2 hat i+ hat j- hat k ,\ 3 hat i-2 hat j+ hat k\ a n d\ hat i+4 hat j- hat k` respectively. These points
a.Form an isosceles triangle b.Form a right triangle c.Are collinear d.Form a scalene triangle

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The position vectors of the points P ,\ Q ,\ R are hat i+2 hat j+3 hat k ,\ -2 hat i+3 hat j+5 hat k\ a n d\ 7 hat i- hat k respectively. Prove that P ,\ Q\ a n d\ R are collinear points.

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

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 vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k form the vertices of a right angled triangle.

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.

Dot product of a vector with hat i+ hat j-3 hat k ,\ hat i+3 hat j-2 hat k\ a n d\ 2 hat i+ hat j+4 hat k are 0, 5 and 8 respectively. Find the vector.

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the 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.

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.

Show that the vector 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k ,\ 3 hat i-4 hat j-4 hat k form the sides of a rights angled triangle.

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. Find a vector vec a of magnitude 5sqrt(2) making an angle of pi/4 wit...

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  2. Write a unit vector in the direction of vec P Q ,\ w h e r e\ P\ a n ...

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  3. Find a vector in the direction of vector 2 hat i-3 hat j+6 hat k which...

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  4. It | vec a|=4\ and-3lt=lambdalt=2, then write the range fo lambda |vec...

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  5. In a triangle OAC, if B is the mid point of side AC and vec O A= vec ...

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  6. If in a "Delta"A B C ,\ A=(0,0),\ B=(3,3sqrt(3)), C-=(-3sqrt(3),3) the...

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  7. If vec a ,\ vec b are the vectors forming consecutive sides of a reg...

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  8. Evaluate int\tan^2x\dx

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  9. If points A(60 hat i+3 hat j),\ B(40 hat i-8 hat j)a n d\ C(a hat i-52...

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  10. If G is the intersection of diagonals of a parallelogram A B C D and O...

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  11. The vector cosalpha\ cosbeta hat i+cosalpha\ sinbeta hat j+sinalpha ha...

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  12. In a regular hexagon A B C D E F ,\ A vec B=a ,\ B vec C= vec b\ a n d...

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  13. The vector equation of the plane passing through vec a ,\ vec b , ve...

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  14. If O\ a n d\ O^(prime) are circumcentre and orthocentre of \ A B C ,\ ...

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  15. If vec a ,\ vec b ,\ vec c and vec d are the position vectors of p...

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  16. Let G be the centroid of triangle\ A B Cdot If vec A B= vec a ,\ ve...

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  17. If A B C D E F is a regular hexagon, them vec A D+ vec E B+ vec F C e...

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  18. The position vectors of the points A ,\ B ,\ C are 2 hat i+ hat j- hat...

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  19. If three points A ,\ B ,\ a n d\ C have position vectors hat i+x hat ...

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  20. A B C D isa parallelogram with A C\ a n d\ B D as diagonals. Then, ve...

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