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Find the vector equation in scalar produ...

Find the vector equation in scalar product form of the plane
`vecr=2hati-hatj+lambda(hati+2hatj+3hatk)+mu(2hati-hatj-3hatk)`.

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Find the vector equation of the following plane in scalar product form: vecr=hati-hatj+lambda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)

Find the vector equation of the following planes in scalar product form: vecr=2hati-hatk+lambdahati+mu(hati-2hatj-hatk) .

Find the shortest distance between the following lines whose vector equations are : vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk)

Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(hati – 2hatj+3hatk) in the scalar dot product form is

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Find the shortest distance between the following lines whose vector equations are : vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk)

Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3hatk

Find the scalar projection of : veca=3hati-2hatj+hatk on vecb=hati-2hatj-3hatk .

Find the shortest distance between the following lines whose vector equations are : vecr=(hati-hatj+2hatk)+lambda(-2hati+hatj+3hatk) and vecr=(2hati+3hatj-hatk)+mu(3hati-2hatj+2hatk)

Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Find the vector equation in scalar product form of the plane vecr=2hat...

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  2. Find the points on z-axis which are at a distance of sqrt21 from the p...

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  3. Find k so that the distance between the points (7, 1, - 3) and (4,5, k...

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  4. Find the point on x-axis which is equidistant from the point (1,3,2) a...

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  5. Find the point which is equidistant from the points (a,0,0),(0,b,0),(0...

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  6. Show that the points (2,4,3),(4,1,9) and (10,-1,6) are the vertices of...

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  7. Find the locus of a point which is equidistant from the points (3,2,1...

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  8. Find the point in the XY-plane which is equidistant from the points (2...

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  9. Prove that the point A (0,0,0),B(2,0,0),C(1,sqrt3,0) and D(1,1/sqrt3, ...

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  10. Find the coordinates of the point which divides the join of the points...

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  11. Find the points on the line segment PQ situated at 2/3 of the distan...

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  12. Find the points on the line segment PQ situated at 2/3 of the distan...

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  13. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

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  14. If A and B are two points whose position vectors are 3hati+2hatj-2hatk...

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  15. Find the coordinates of the point which is three fifth of the way (3,4...

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  16. Find the ratio in which the line segment joining : (1,2,3) and (-3,4,-...

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  17. If A and B are the points (-3,4,-8) and (5,-6,4) respectively, find th...

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  18. Using section formula, prove that the three points (-2,3,5),(1,2,3) an...

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  19. Show that the points : (4, 7, 8), (2, 3, 4), (- 1, - 2, 1), (1, 2, 5) ...

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  20. Using vectors, show that the medians of a triangle are concurrent.

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  21. Prove that the points A(5,0,2), B(2,-6,0),C(4,-9,6) and D(7,-3,8), tak...

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