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If `2hati-hatj+3hatk,3hati+2hatj+hatk,hati+mhatj+4hatk` are coplanar, find the value of m.

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` -3 `
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If vectors veca =hati +2hatj -hatk, vecb = 2hati -hatj +hatk and vecc = lamdahati +hatj +2hatk are coplanar, then find the value of (lamda -4) .

If veca=2hati+3hatj-hatk, vecb= -hati+2hatj-4hatk, vec c =hati+hatj+hatk , then find the value of (veca xx vecb)*(veca xx vec c) .

Show that the points whose position vectors 4hati + 5hatj + hatk, -hatj -hatk, 3hati + 9hatj + 4hatk and -4hati + 4hatj + 4hatk are coplanar.

Show that the lines vecr=(-2hati-4hatj-6hatk)+t(hati+4hatj+7hatk) vecr=(hati+3hatj+5hatk)+s(3hati+5hatj+7hatk) are coplanar. Find the equation of such plane in non parametric form and in cartesian form.

veca=hati-hatj+hatk, vecb=2hati+hatj-hatk, vec c=lambda hati-hatj+lambda hatk are coplanar then lambda is :

Prove that the points 2hati+3hatj+4hatk,3hati+4hatj+2hatk,4hati+2hatj+3hatk from an equilateral triangle.

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FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
  1. If 2hati-hatj+3hatk,3hati+2hatj+hatk,hati+mhatj+4hatk are coplanar, fi...

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  2. The work done by the force vecF=ahati+hatj+hatk in moving the point...

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  3. If the position vectors of three points A, B and Care respectively v...

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  4. A force given by and 3veci+2vecj-4veck is applied at the point (1,-1...

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  5. Show that the area of a parallelogram having diagonals 3veci+vecj-2v...

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  6. If the edges  veca=-3veci+7vecj+5veck , vecb=-5veci+7vecj-3veck ,...

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  7. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

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  8. The volume of the parallelepiped whose edges are represented by -12 ha...

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  9. Prove that |vecavecbvecc|=abc   if and only if veca , vecb , ...

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  10. Show that the points (1, 3, 1), (1, 1,-1), (-1, 1, 1), (2,2, -1) are l...

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  11. If veca=2veci+3vecj-5veck , vecb=-veci-vecj+2veck and vecc=4vec...

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  12. If veca =3veci+2vecj-4veck , vecb =5veci-3vecj+6veck , vecc =5ve...

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  13. If veca =2veci+3vecj-veck , vecb =2veci+5veck , vecc =vecj-3veck...

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  14. Find the vector and cartesian equations of the straight line passing t...

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  15. Find the vector and cartesian equations of the straight line passing t...

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  16. Find the angle between the following lines vecr=3veci+2vecj-veck+t(v...

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  17. Find the angle between the following lines (x-1)/(2)=(y+1)/(3)=(z-4)...

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  18. Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-...

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  19. Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hat...

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  20. Show that the lines (x-1)/(3)=(y-1)/(-1)=(z+1)/(0) and (x-4)/(2)=...

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  21. find the shortest distance between the skew lines. vecr=(veci-vecj)+...

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