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Find a unit vector perpendicular to each...

Find a unit vector perpendicular to each of the vectors `hat i+2 hat j+3 hat k` and `-3 hat i-2 hat j+hat k`. Also find the area of the parallelogram determined by these vectors.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find a unit vector perpendicular to the plane of two vectors a=hat(i)-...

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  2. Find the equation of a plane through the points (3,-1,2), (1,-1,-3) an...

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  3. Find a unit vector perpendicular to each of the vectors hat i+2 hat j+...

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  4. Find the sine of the angle between the vectors : (3,0,3) and (1,2,-7)

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  5. Find the sine of the angle between the vectors : 2 hat i+ 4 hat j+ 4 ...

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  6. Determine the area of the parallelogram whose adjacent sides are the ...

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  7. Find the area of the parallelogram having two adjacent sides OA and OB...

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  8. Find the area of triangle PQR where P,Q,R have respectively coordinate...

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  9. Find the area of the triangle formed by O,A,B where : vec OA= hat i+ ...

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  10. Find the area of the triangle formed by O,A,B where : vec OA= 3 hat i...

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  11. If vec axx vec b= vec cxxvec d and vec axx vec c= vec bxxvec d, show t...

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  12. Find the area of the triangle ABC where A,B,C are the points (a,0,0), ...

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  13. Find the area of the triangle having the points A(1,1,1), B(1,2,3) and...

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  14. If vec a= 2 hat i+ hat j- hat k, vec b= -hat i+ 2 hat j- 4 hat k and v...

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  15. Calculate the product ((hat i- 2 hat j+ 3 hat k) cross (2 hat i+ hat j...

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  16. If vec a= hat i- 2 hat j+ hat k, vec b= 2 hat i - hat j+ hat k and vec...

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  17. Define the vector product of two vectors vec a and vec b. If vec a = 2...

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  18. If vec a= 2 hat i+ 5 hat j- 7 hat k, vec b= -3 hat I + 4 hat j+ hat k ...

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  19. If G is the centroid of triangle ABC, prove that area triangle AGB = ...

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  20. If D, E, f are the mid-point of the sides of triangle ABC, prove that ...

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