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What is the direction of (hati+hatj+hatk...

What is the direction of `(hati+hatj+hatk)+(hati+hatk-3hatj)+ (hatk+hati-3hatj)+(hati+hatj-3hatk)` ?

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

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

Find the unit vector in the direction of 6hati +2hatj +3hatk .

What is the value of a so that 6hati+2hatj-3hatk and hati-4hatj+ahatk are orthogonal to each other ?

Write a unitvector in the direction of the sum of vectors veca=2hati-hatj-2hatk and vecb=-hati+hatj+3hatk

The position vectors of the points A, B, C and D are 4hati+3hatj-hatk , 5hati+2hatj+2hatk , 2hati-2hatj-3hatk and 4hati-4hatj+3hatk respectively. Show that AB and CD are parallel.

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. If veca and vecb are unit vectors such that vecaxxvecb is a unit vecto...

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

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  3. What is the direction of (hati+hatj+hatk)+(hati+hatk-3hatj)+ (hatk+hat...

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  4. What is the projection of hat i + hat j - hat k upon the vector hat i ...

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  5. Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

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  6. Let vec(a) = hat(i) + hat(j) + hat(k), vec(b) = 4hat(i) - 2hat(j) + 3h...

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  7. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  8. If veca+vecb+vecc = vec0, |veca| = 3 , |vecb| = 5 and |vecc| = 7, find...

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  9. The position vectors of the points A, B, C and D are 4hati+3hatj-hatk,...

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  10. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  11. If veca = (2,-2,1), vecb = (2,3,6) and vecc = (-1,0,2), Find the magni...

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  12. Prove the following by vector method. An angle inscribed in a semi-cir...

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  13. If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbx...

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  14. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  15. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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  16. Find a vectorvecb such that vecaxxvecb=vecc and veca.vecb = 3 where ve...

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  17. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  18. Determine the area of the parallelogram whose sides are the vectors 2h...

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  19. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  20. Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...

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