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If hati+hatj+hatk,2hati+5hatj,3hati+2hat...

If `hati+hatj+hatk,2hati+5hatj,3hati+2hatj-3hatkandhati-6hatj-hatk` are position vectors of points A,B,C and D respectively , then find the angle between `vec(AB)andvec(CD)`. Deduce that `vec(AB)andvec(CD)` are collinear.

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If the position vectors of the points A, B, C, D are hati+hatj+hatk, 2hati+5hatj, 3hati +2hatj-3hatk and hati-6hatj-hatk respectively, then the angle between the vectors vec(AB) and vec(CD) is -

Show that the vectors 2hati-3hatj+4hatkand-4hati+6hatj-8hatk are collinear.

vecA =2hati+3hatj+4hatk and vecB=hati-hatj+hatk are two vectors. Find vecAxxvecB .

If vecA= 5hati+6hatj+3hatk and vecB=6hati-2hatj-6hatk , then

Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7hati-hatk) are collinear.

Show that the vectors hati -2 hatj+3hatk , -2hati+3hatj-4hatk and hati -3hatj +5hatk are coplanar.

Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

If veca=hati+3hatj+hatk, vecb=2hati-hatj-hatk and vec c=m hati+7hatj+3hatk are coplanar, then the value of m is -

Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk form the vertices of a right angled triangle.

For what value of a, the vectors 2hati-3hatj+4hatk and a hati-6hatj+8hatk are collinear ?

NCERT BANGLISH-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10
  1. If hati+hatj+hatk,2hati+5hatj,3hati+2hatj-3hatkandhati-6hatj-hatk are...

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  2. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

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  3. Find the scalar components and magnitude of the vector joining the poi...

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  4. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  5. If veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

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  6. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

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  7. Find a vector of magnitude 5 units and parallel to the resultant of th...

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  8. If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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  9. Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , ...

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  10. Find the position vector of a point R which divides the line joining t...

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  11. The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2h...

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  12. Show that the direction cosines of a vector equally inclined to the ax...

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  13. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4ha...

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  14. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  15. If with reference to the right handed system of mutually perpendicular...

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  16. Prove that (veca+vecb)*(veca+vecb)=|veca|^(2)+|vecb|^(2), if and only...

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  17. If theta is the angle between two vectors vecaandvecb then veca*vecbge...

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  18. Let vecaandvecb be two unit vectors and theta is the angle between the...

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  19. The value of hati*(hatk xx hatj) + hatj*(hati xx hatk)+hatk*(hatj xx h...

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  20. If theta is the angle between any two vectors vecaandvecb, then |veca*...

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