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Evaluate the following products: (3 hat ...

Evaluate the following products: `(3 hat i-6 hat j+2 hat k)*(2 hat i+hat j-2 hat k)`.

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Evaluate the following products: (2 hat i+3 hat j)*(-hat i+3 hat j +hat k) .

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

Find a unit vector perpendicular to both the vectors (3 hat i + 2 hat j - hat k) and ( hat i + 2 hat j + hat k) .

Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+lambda( hat i- hat j+ hat k) and the plane vec r = dot(2 hat i- hat j+ hat k)=4.

Find the angle between the vectors 3 hat i-2 hat j -6 hat k and 4 hat i-hat j-8 hat k .

Find the magnitude of vec a=(hat i+3 hat j- 2 hat k)*(-hat i+3 hat k) .

Find the unit vector in the direction of sum of vectors -2 hat i- 3 hat j+ 2 hat k , 3 hat i+ 4 hat j- 2 hat k and hat i+ 2 hat j+ 6 hat k .

Prove that the points whose position vectors are hat i - hat j+ hat k , 2 hat i+ 3 hat j+ hat k , hat i+ 2 hat j+ 3 hat k , -2 hat j+ 3 hat k lie in the same plane.

Show that the points A(-2 hat i+ 3 hat j + 5 hat k) , B(hat i+ 2 hat j+ 3 hat k) and C(7 hat i-hat k) are collinear.

Find λ and μ if (2 hat i + 6 hat j+27 hat k) xx (hat i +λ hat j +μ hat k) = vec 0

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find vec a* vec b if vec a= 2 hat i+ hat k and vec b= hat i+hat j+hat ...

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  2. If vec a=4 hat i+3 hat j+hat k and vec b=hat i-2 hat k, find | vec a *...

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  3. Evaluate the following products: (3 hat i-6 hat j+2 hat k)*(2 hat i+ha...

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  4. Evaluate the following products: (2 hat i+3 hat j)*(-hat i+3 hat j +ha...

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  5. Evaluate the following products: (2,-1,1)*(3,4,-1).

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  6. Taking vec a= 2 hat i-3 hat j- hat k and vec b=hat i+4 hat j-2 hat k, ...

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  7. If vec a=3 hat i+4 hat j and vec b=hat i-hat j+hat k, find the value o...

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  8. Find the magnitude of vec a=(hat i+3 hat j- 2 hat k)*(-hat i+3 hat k).

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  9. Given |quad vec a|=10,|quad vec b|=2 and vec a *vec b=12, find | vec a...

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  10. Define vec a*vec b where vec a and vec b are any two vectors. Find ve...

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  11. Find a unit vector perpendicular to both the vectors hat i-2 hat j+3 h...

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  12. Find a unit vector perpendicular to both the planes of vec a and vec b...

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  13. Find a unit vector perpendicular to the plane of two vectors a=hat(i)-...

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

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

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

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

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

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

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

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