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Show that the vectors 2hati + 3hatj,5hat...

Show that the vectors `2hati + 3hatj,5hati -5hatk` and `6hatj + 4hatk` are co-planar.

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Show that the vectors 4hati+4hatj+ 4hatk,7hati+6hatj-hatk and 3hati+2hatj-5hatk form a right angled triangle and find its area.

Prove that the vectors 2hati-hatj+hatk , hati-3hatj-5hatk , 3hati-4hatj-4hatk are the sides of a right angled triangle.

Prove that four points with position vectors hati+hatj-3hatk, 2hati -hatj-hatk,- hati +2hatj +2hatk and 2hati +2hatk arecoplanar

If the vectors veca = 2hati + 3hatj +-6hatk and vecb = alphahati-hatj +2hatk are parallel, then alpha = ______

What is the value of x so that the vector 6hati+2hatj-3hatk and hati-4hatj+xhatk are perpendicular to each other.

Find the value of lambda so that three vectors veca=2hati-hatj+hatk, vecb=hati+2hatj-3 hatk and vecc= 3hati +lambda vecj+5 hatk are coplanar.

Write a vector normal to hati+hatk and hati+hatj .

Find the value of 'a' do the which the pointA,B,C with position vectors 2hati-hatj+hatk,hati-3hatj-5hatk and ahati-3hatj+hatk respectively are the vertices of a right angled triangle with /_C=pi/2 .

Find the angle between the vectors 3hati+ 4hatj and 2hati+hatj+hatk .

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. What is the volume of the parallelopiped whose sides are given by the ...

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  2. Write the values of m and n for which the vectors (m-1)overset^i+(n+2)...

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  3. Show that the vectors 2hati + 3hatj,5hati -5hatk and 6hatj + 4hatk are...

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  4. If A, B, C, D, E are the.vertices of a regular pentagon, find the vect...

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  5. If vec(a).vec(b) = 0 and vec(a) xx vec(b) = vec(0), then draw the conc...

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  6. Find a vector in the direction of vector 2hati-3hatj+6hatk which has m...

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  7. Find the unit vector in the direction of the sum of the vectors veca=2...

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  8. Write a unitvector in the direction of the sum of vectors veca=2hati-h...

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  9. If veca =xhati+2hatj-zhatk, vecb=3hati-yhatj+2hatk are two equal vecto...

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  10. If hata.hatb=1/2then what is the angle between hata and hatb?

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  11. Write the value of the cosine of the angle which the vector veca =hati...

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  12. Write a vector in the direction of the vector hati-2hatj+3hatk that ha...

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  13. Find the value of ‘a’ such that the vector 6hati+2hatj-3hatk is perpen...

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  14. What is the unit vector perpendicular to the vectors hati- hatj and 2h...

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  15. What is the magnitude of 2veca xx 3veca ?

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  16. If (vec a times vec b)^2 + (vec a cdot vec b)^2=144, write the value o...

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  17. Write a vector normal to hati+hatk and hati+hatj.

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  18. What is the angle between hati+ hatj and hati-hatj ?

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  19. If veca and vecb are unit vectors such that vecaxxvecb is a unit vecto...

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  20. If two vectors oversetrarra and oversetrarrb are such that |oversetrar...

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