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Show that the vectors 2hati-hatj+4hatk a...

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

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Let, `veca = 2hati-3hatj+4hatk` and `vecb = -4hati+6hatj-8hatk = -2(2hati-3hatj+4hatk) = -2veca`.
One vector can be expressed in terms of another. Therefore `veca&vecb` are collinear.
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MAHAVEER PUBLICATION-VECTOR-QUESTION BANK
  1. Show that (hati-hatj)/sqrt2 is a unit vector.

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  2. Find the direction ratios and direction cosines of the vector veca = h...

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

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  4. Find |vecx|, if for a unit vector veca, (vecx-veca).(vecx+veca) = 12.

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  5. Find |veca-vecb|, if two vectors veca and vecb are such that |veca| = ...

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  6. If = veca = hati-7hatj+7hatk and vecb = 3hati-2hatj+2hatk find vecaxxv...

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  7. Evaluate (3veca-5vecb).(2veca+7vecb)

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  8. Find lambda and mu if (2hati+6hatj+27hatk)xx(hati+lambdahatj+muhatk) =...

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  9. Show that, (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb).

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  10. Find the scalar triple product vectors hati+2hatj+3hatk, hati-hatj+hat...

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  11. Find lambda if the vectors hati+hatj+2hatk, lambdahati-hatj+hatk and 3...

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  12. Show that the points A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1) are colli...

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  13. Show that the points with position vectors hati+2hatj+7hatk, 2hati+6ha...

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  14. Find the angle between the vectors hati-2hatj+3hatk and 3hati-2hatj+ha...

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  15. Show that the vectors 1/7(2hati+3hatj+6hatk), 1/7 (3hati-6hatj+2hatk) ...

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  16. If veca = 5hati-hatj-3hatk, vecb = hati+3hatj-5hatk then show that the...

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  17. If veca = 2hati+2hatj+3hatk, vecb = -hati+2hatj+hatk and vecc = 3hati...

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  18. Find x,y,z if hati+hatj+2hatk, -hati+zhatk and 2hati+xhatj+yhatk are m...

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  19. Find a vector and unit vector perpendicular to each of the vector veca...

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  20. Find a vector of magnitude 11 in the direction opposite to that of vec...

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