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If three points `A ,\ B ,\ a n d\ C` have position vectors ` hat i+x hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k\ a n d\ y hat i-2 hat j-5 hat k` respectively are collinear, them `(x , y)=` a.`(2,-3)` b. `(-2,3)` c. `(-2,-3)` d. `(2,3)`

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If three points A, B and C with position vectors hat(i) + x hat(j) +3 hat(k) , 3 hat(i) + 4 hat(j) + 7hat( k) and y hat(i) - 2 hat(j) - 5 hat(k) respectively are collinear, then (x,y) =

Prove that the points having position vectors hat i+2 hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k ,\ -3 hat i-2 hat j-5 hat k are collinear.

Show that the points whose position vectors are 5 hat i+5 hat k ,\ 2 hat i+ hat j+3 hat k\ a n d-4 hat i+3 hat j- hat k are collinear.

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

For what value of a the vectors 2 hat i-3 hat j+4 hat k\ a n d\ a hat i+6 hat j-8 hat k are collinear?

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

Show that the four points A, B, C and D with position vectors 4 hat i+5\ hat j+ hat k ,-(\ hat j+ hat k),3 hat j+9\ hat j+4 hat k\ a n d\ 4( hat i+ hat j+ hat k) , respectively are coplanar.

Prove that the following vectors are coplanar: 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k\ a n d\ 3 hat i-4 hat j-4 hat k

Show that the vectors veca= hat i-2 hat j+3 hat k , vecb=-2 hat i+3 hat j-4 hat ka n d vec c= hat i-3 hat j+5 hat k are coplanar.

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.

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
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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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