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Show that the vectors a =3hati - 2hatj+h...

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

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Using dot product of vectors show that the vectors 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk form a righat angled triangle

Prove that the vectgors 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk form a righat angled triangle.

The three vectors vecA=3hati-2hatj+hatk, vecB=hati-3hatj+5hatk and vecC=2hati+hatj-4hatk form

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

The three vectors vecA=3hati-=2hatj+khat,vecB=hati-3hatj+5hatk and vec C=2hati+hatj-4hatk form

Prove that the points 2hati-hatj+hatk, hati-3hatj-5hatk and 3hati-4hatj-4hatk are the vertices of a righat angled triangle. Also find the remaining angles of the triangle.

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Show that the vectors hati-3hatj+2hatk, 2hati-4hatj-hatk and 3hati+2hatj-hatk are linearly independent

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

The three vectors vecA=3hati-2hatj-hatk,barB=hati-3hatj+5hatk and barC=2hati-hatj-4hatk does not form

SL ARORA-VECTORS-Problems For Self Practice
  1. A force vec(F) = 5hati + 4hatj newton displaces a body through vec(S) ...

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  2. If the resultant of the vectors 3 hati +4 hatj +5 hatk and 5 hati +3 h...

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  3. Show that the vectors a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk and ...

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  4. If vectors vec(A),vec(B) and vec(C) have magnitudes 8,15 and 17 units ...

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  5. If vec A =vec B- vec C, then determine the angle between vec A and ve...

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  6. For two vectors vec(A) and vec(B) if vec(A) + vec(B) = vec(C) and A +B...

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  7. Prove that (vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos the...

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  8. Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 ha...

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  9. If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk, th...

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  10. Find the value of a for which the vectors 3 hati + 3hatj + 9 hatk and ...

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  11. Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3...

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  12. Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj...

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  13. Find a vector of magnitude 18 which is perpendicular to both the vecto...

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  14. Determine the area of the parallelogram whose adjacent sides are forme...

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  15. Find the area of the triangle formed by points O,A and B such that vec...

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  16. Find with the help of vectors, the area of the triangle with vertices ...

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  17. If vec(A) and vec(B) are two such vectors that |vec(A)| = 2, |vec(B)| ...

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  18. Find the moment about the point hati + 2hatj - hatk of a force represe...

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  19. Prove that (vec(a) + vec(b)) xx (vec(a) - vec(b)) = 2 (vec(b) xx vec(a...

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  20. Prove that |vec(a) xx vec(b)| = sqrt(a^(2)b^(2) -(vec(a) -vec(b))^(2))

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