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Area of a rectangle having vertices A [-...

Area of a rectangle having vertices `A [- hat i +1/2 hat j +4 hat k], B[hat i +1/2 hat j +4 hat k] ,C[hat i -1/2 hat j +4 hat k]` and `D [- hat i -1/2 hat j +4 hat k]` is

A

`1/2`

B

1

C

2

D

4

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Find the shortest distance between the lines given by the equations vec r= (hat i + 2 hat j + 3 hat k + lambda (2 hat i + 3 hat j + 4 hat k) , vec r= (2 hat i - 4 hat j + 5 hat k + mu (3 hat i - 4 hat j + 5 hat k) .

Prove that the vectors 2 hat i- hat j+ hat k , hat i- 3 hat j- 5 hat k and 3 hat i- 4 hat j- 4 hat k are coplanar.

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.

Show that the point A,B,C and D whose position vectors are respectively 2 hat i+ 4 hat j+ 2 hat k , hat i+ 2 hat j+ hat k , 3 hat i+ hat j- 3 hat k and 4 hat i+3 hat j - 2 hat k are the vertices of a paralleogram (use vector method).

Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +4hat j - hat k

Show that the vectors 2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j -8 hat k are collinear.

Find the shortest distance between the lines vec r = (hat i + 2 hat j + hat k) + lambda (hat i - hat j + hat k) and vec r = ( 2 hat i - hat j - hat k) + mu ( 2 hat i + hat J + 2 hat k)

Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and hat i+ λ hat j- 3 hat k are coplanar.

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.

Find vec a* vec b if vec a=3 hat i+4 hat j-2 hat k and vec b=-2 hat i+ 2 hat j + hat k

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the area of the parallelogram whose adjacent sides are determined...

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  2. Let the vectors vec and vec b be such that |vec a|= 3 and |vec b|= sqr...

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  3. Area of a rectangle having vertices A [- hat i +1/2 hat j +4 hat k], B...

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  4. Find [vec a, vec b, vec c] if vec a= hati -2 hat j+ 3 hat k, vec b=2 h...

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  5. Show that the vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + ...

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  6. Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and ...

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  7. Let vec a= hat i+ hat j+ hat k and vec b = hat i and vec c=c1 hat i + ...

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  8. Let vec a= hat i+ hat j+ hat k and vec b = hat i and vec c=c1 hat i + ...

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  9. Show that the four points with position vectors 4hati+8 hat j +12hat k...

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  10. Find 'x' such that the four points : A(3,2,1),B(4,x,5),C(4,2,-2) and D...

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  11. If a,b and c are coplanar show "[a+b b+c c+a]" are coplanar.

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  12. Write down a unit vector in XY-plane, making an angle of 30^o with the...

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  13. Find the scalar components and magnitude of the vector joining the poi...

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  14. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  15. If vec a= vec b + vec c then is it true that |vec a|= |vec b|+ |vec c|...

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  16. Find the value of x for which x (hat i +hat j +hat k) is a unit vector...

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  17. Find a vector of magnitude 5 units, and parallel to the resultant of t...

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

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  19. Show that the points A (1, - 2, - 8), B (5, 0,- 2) and C (11, 3, 7) ar...

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  20. Find the position vector of a point R which divides the line joining t...

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