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Show that the points A(-2hati+3hatj+5hat...

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

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Show that the points vectors are 2hati+3hatj-5hatk,3hati+hatj-2hatk and 6hati-5hatj+7hatk are collinear.

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

Examine whether the vectors hati+3hatj+hatk,2hati-hatj-hatk and 7hatj+5hatk are coplanar.

Determine whether the three vectors 2hati+3hatj+hatk, hati-2hatj+2hatk and 3hati+hatj+3hatk are coplanar.

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

Show that the lines vecr=(6hati+hatj+2hatk)+s(hati+2hatj-3hatk) and vecr=(3hati+2hatj-2hatk)+t(2hati+4hatj-5hatk) are skew lines and hence find the shortest distance between them.

Prove that points hati+2hatj-3hatk, 2hati-hatj+hatk and 2hati+5hatj-hatk form a triangle in space.

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

NCERT TAMIL-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10
  1. Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7ha...

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

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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 = vec b+ vec c, then is it true that |veca| = |vec b| + |vec ...

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  6. Find the value of x for which x (hat i + hat j + hat k) is a unit vect...

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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=2hati-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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

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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 2 hat i - 4 hat j + 5 ha...

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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. Thescalar product of the vector hat i + hat j + hat k with a unit vect...

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  15. If veca,vecb,vecc are mutually perpendicular vectors of equal magnitu...

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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.(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjxxhati) ...

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  20. If theta is the angle between any two vectors vec a and vec b , then |...

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