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Show that the vectors vec a= hat i- 2hat...

Show that the vectors `vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + 3hat j- 4hat k and vec c =hat i - 3 hat j+5 hat k` are coplanar.

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Prove that the vectors vec a = hat i- 2 hat j+ hat k , vec b= -2 hat i+ hat j+ hat k and vec c= hat i+ hat j-2 hat k are coplanar.

Show that the vectors vec a = hat i- 3 hat j+ 2 hat k , vec b= 2 hat i- 4 hat j- 4hat k and vec c= 3 hat i+ 2 hat j- 3hat k are linearly independent.

Find λ such that the vectors vec a =hat i +3 hat j +hat k, vec b= 2 hat i -hat j - hat k and vec c= λ hat i +7 hat j +3 hat k are coplanar.

Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 hat i +22 hat j- 2 hat k and vec c = 2hat i -8 hat j +16hat k are coplanar.

Find λ such that the vectors vec v_1 =2 hat i - hat j +hat k, vec v_2= hat i +2hat j -3 hat k and vec v_3= 3 hat i +λ hat j +5 hat k are coplanar.

Find the value of scalar λ if the vectors vec a =2 hat i +hat j +hat k, vec b= hat i -hat j+2hat k and vec c =λ hat i +3 hat j -2 hat k are coplanar.

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = 2 hat i- 3 hat j + 4 hat k, vec b= hat i +2 hat j- hat k and vec c = 3 hat i -hat j +2 hat k .

Prove that the vectors vec a= hat i- 3 hat j - 5 hat k , vec b= 2 hat i- hat j+ hat k and vec c= hat i+ 2 hat j+ 6 hat k from of a right angled triangle.

Find the volume of the Parallelopiped whose coterminous edges are represented by the vectors vec a = -3hat i+7 hat j + 5 hat k, vec b=-5 hat i +7 hat j- 3 hat k and vec c = 7 hat i -5 hat j -3 hat k .

Find λ if vectors vec a = hat i +λ hat j +hat k, vec b= 2hat i -hat j-hat k and vec c =7 hat j +3hat k are coplanar.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Show that the direction cosines of a vector equally inclined to the ax...

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