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Find the area of the triangle formed by `O ,\ A ,\ B\ w h e n\ O A= hat i+2 hat j+3 hat k ,\ O B=-3 hat i-2 hat j+ hat kdot`

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Find the area of the triangle formed by (O,A)/(OA),B when vec OA=hat i+2hat j+3hat k,vec OB=-3hat i-2hat j+hat k

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Find the area of the parallelogram determined by the vectors: 2hat i and 3hat j2hat i+hat j+3hat k and hat i-hat j3hat i+hat j-2hat k and hat i-3hat j+4hat khat i-3hat j+hat k and hat i+hat j+hat k

Find a unit vector perpendicular to each of the vector -> a+ -> b and -> a- -> b where -> a=3 hat i+2 hat j+2 hat k and -> b= hat i+2 hat j-2 hat k

Find the area of the parallelogram whose diagonals are 2hat i+hat j and hat i+hat j+hat k

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Show that each of the following triads of vectors are coplanar: vec a= hat i+2 hat j- hat k , vec b=3 hat i+2 hat j+7 hat k , vec c=5 hat i-6 hat j+5 hat k vec a=-4 hat i-6 hat j-2 hat k , vec b=- hat i+4 hat j+3 hat k , vec c=8 hat i- hat j+3 hat k hat a= hat i-2 hat j+3 hat k , vec b=-2 hat i+3 hat j-4 hat k , vec c= hat i-3 hat j+5 hat k

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

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RD SHARMA-VECTOR OR CROSS PRODUCT -Solved Examples And Exercises
  1. prove that | vec axx vec b|=( vec adot vec b)t a ntheta,\ w h e r e\ t...

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  2. If | vec a|=sqrt(26),\ | vec b|=7\ a n d\ | vec axx vec b|=35 ,\ fin d...

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  3. Find the area of the triangle formed by O ,\ A ,\ B\ w h e n\ O A= hat...

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  4. Let vec a= hat i+4 hat j+2 hat k ,\ vec b=3 hat i-2 hat j+7 hat k\ a...

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  5. Find a unit vector perpendicular to each of the vectors vec a+ vec b\...

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  6. Using vectors, find the area of triangle with vertices A(2,3,5), B(3,5...

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  7. If vec a=2 hat i-3 hat j+ hat k ,\ vec b=- hat i+ hat k ,\ vec c=2 ...

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  8. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

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  9. If either -> a= ->0 and -> b= ->0 then -> axx -> b= ->0 . Is ...

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  10. If vec a=a1 hat i+a2 hat j+a3 hat k ,\ vec b=b1 hat i+b2 hat j+b3 ha...

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  11. Using vectors, find the area of the triangle with vertices A(1,1,2),\ ...

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  12. Find all vectors of magnitude 10sqrt(3) that are perpendicular to the ...

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  13. Define vector product of two vectors.

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  14. Write the value ( hat ixx hat j)dot hat k+ hat idot hat jdot

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  15. Write the value of hat idot( hat jxx hat k)+ hat jdot( hat kxx hat i)...

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  16. Write the value of hat idot( hat jxx hat k)+ hat jdot( hat kxx hat i)...

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  17. Write the value of hat ixx( hat j+ hat k)+ hat jxx( hat k+ hat i)+ ha...

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  18. Write the expression for the area of the parallelogram having vec a\ ...

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  19. If vec a\ a n d\ vec b are unit vectors then write the value of | ve...

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  20. If vec a\ a n d\ vec b are two vectors of magnitudes 3 and (sqrt(2))...

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