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Prove that |vec(a) xx vec(b)|=(vec(a)*ve...

Prove that `|vec(a) xx vec(b)|=(vec(a)*vec(b)) tan theta," where " theta `is the angle between `vec(a) and vec(b)`.

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`(vec(a) xx vec(b)) = |vec(a)| | vec(b)| sin theta * hat(n)`
`rArr | vec(a) xx vec(b)|=ab sin theta , " where " | vec(a)|=and |vec(b)|=b`
`=(ab cos theta) ( tan theta)=( vec(a)* vec(b)) tan theta.`
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RS AGGARWAL-CROSS,OR VECTOR, PRODUCT OF VECTORS-Exercise 24
  1. Find a vector of magnitude 6 which is perpendicular to both the vector...

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  2. Find a unit vector perpendicular to each of the vectors ( -> a+ -> ...

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  3. Find the angle between two vectors vec(a) and vec(b) with magnitudes 1...

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  4. Let vec a= hat i- hat j ,\ vec b=3 hat j- hat k and vec c=7 hat i- h...

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  5. If vec(a)=(4hat(i)+ 5 hat(j) - hat(k)),vec(b)=(hat(i)-4 hat(j)+ 5 hat(...

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  6. Prove that |vec(a) xx vec(b)|=(vec(a)*vec(b)) tan theta," where " the...

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  7. Write the value of p for which vec a=3 hat i+2 hat j+9 hat k\ a n d\ ...

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  8. verify thatvec(a) xx (vec(b)+ vec(c))=(vec(a) xx vec(b))+(vec(a) xx ve...

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  9. Find the area of the parallelogram whose adjacent sides are represente...

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  10. Find the area of the parallelogram whose diagonals are represented by...

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  11. Find the area of the trinagle whose two adjacent sides are determined ...

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  12. Using vectors, find the area of Delta ABC whose vertices are (i) A...

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  13. Using vector method, show that the given points A,B,C are collinear: ...

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  14. Show that the points A,B,C with position vectors (3hat(i)- 2 hat(j)+ 4...

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  15. Show that the points having position vectors vec(a), vec(b),(vec(c)=3 ...

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  16. Show that the points having position vectors (-2vec(a) + 3 vec(b)+5vec...

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  17. Find a unit vector perpendicular to the plane ABC, where the coordi...

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  18. If vec(a)= ( hat(i)- 2hat(j) + 3hat(k)) and vec(b)=(hat(i)-3hat(k)) ...

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  19. If | vec a|=2,|b|=5 and | vec ax vec b|=8, find vec adot vec bdot

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  20. If |vec(a)| = 2, |vec(b)|= 7 and (vec(a) xx vec(b))=(3 hat(i) + 2 hat(...

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