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Find the values of x & y so that vectors...

Find the values of x & y so that vectors `2hati+3hatj` and `xhati+Yhatj` are equal.

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To find the values of \( x \) and \( y \) such that the vectors \( 2\hat{i} + 3\hat{j} \) and \( x\hat{i} + y\hat{j} \) are equal, we can follow these steps: ### Step 1: Set the vectors equal to each other We have two vectors: - Vector A: \( 2\hat{i} + 3\hat{j} \) - Vector B: \( x\hat{i} + y\hat{j} \) Since these vectors are equal, we can write: ...
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MAHAVEER PUBLICATION-VECTOR-QUESTION BANK
  1. Find the unit vector in the direction of 2hati+3hatj+hatk.\

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  2. Let, veca = hati+2hatj and vecb = 2hati+hatj. If |veca| = |vecb|. Are ...

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  3. Find the values of x & y so that vectors 2hati+3hatj and xhati+Yhatj a...

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  4. Find the scalar and dot product of vectors hati+2hatj-3hatk and 2hati-...

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  5. Show that (hati-hatj)/sqrt2 is a unit vector.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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