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The position vector of the points P an...

The position vector of the points `P` and `Q` are `5 hat i+7 hat j-2 hat k` and `-3 hat i+3 hat j+6 hat k` , respectively. Vector ` vec A=3 hat i- hat j+ hat k` passes through point `P` and vector ` vec B=-3 hat i+2 hat j+4 hat k` passes through point `Q` . A third vector `2 hat i+7 hat j-5 hat k` intersects vectors `A` and `Bdot` Find the position vectors of points of intersection.

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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.

Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on the vector vec b=2 hat i+2 hat j+ hat k .

A line passes through the points whose pdotvdot are hat i+ hat j-2 hat k and hat i-3 hat j+ hat k .The position vector of a point on it at unit distance from the first point is

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Prove that lines vec( r)= (hat(i)+ hat(j) + hat(k))+ t(hat(i) - hat(j) + hat(k)) and vec(r ) = (3hat(i) - hat(k)) + s(4hat(j) - 16hat(k)) intersect. Also find the position vector of their point of intersection

Show that each of the following triads of vectors are coplanar: vec a=-4 hat i-6 hat j-2 hat k ,\ vec b=- hat i+4 hat j+3 hat k ,\ vec c=-8 hat i- hat j+3 hat k .

Show that each of the following triads of vectors are coplanar: vec a= hat i-2 hat j+3 hat k ,\ vec b=-2 hat i+3 hat j-4 hat k ,\ vec c= hat i-3 hat j+5 hat kdot

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.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2 hat i- hat j+4 hat k and is in the direction hat i+2 hat j- hat k .

Show that each of the following triads of vectors are coplanar: vec a= hat i+2 hat j- hat k ,\ vec b=3 hat i+2 hat j+7 hat k ,\ vec c=5 hat i+6 hat j+5 hat k .

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. solve the differential equation (1+x^2)dy/dx=x

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  2. Sow that x1 hat i+y1 hat j+z1 hat k ,x2 hat i+y2 hat j+z2 hat k ,a n d...

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  3. The position vector of the points P and Q are 5 hat i+7 hat j-2 hat ...

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  4. Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat...

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  5. If vec a and vec b are two unit vectors and theta is the angle between...

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  6. The vectors x hat i+(x+1) hat j+(x+2) hat k ,(x+3) hat i+(x+4) hat j+(...

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  7. vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammad...

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  8. The vector vec a has the components 2p and 1 w.r.t. a rectangular C...

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  9. The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 ...

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  10. If vec a , vec b , vec c are non-coplanar vector and lambda is a re...

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  11. If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are...

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  12. If the vectors hat i- hat j , hat j+ hat k and vec a form a triangl...

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  13. If the resultant of three forces vec F1=p hat i+3 hat j- hat k , v...

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  14. vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c...

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  15. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

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  16. Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k ...

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  17. Show that the point A , B and C with position vectors vec a =3 hat i ...

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  18. If 2vec(AC)=3vec(CB), then prove that 2vec(OA)+3vec(OB)=5vec(OC) where...

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  19. Find the unit vector in the direction of vector vec (PQ), where P and...

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  20. For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + ...

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