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Let the vectors vec a, vec b, vec c be g...

Let the vectors `vec a, vec b, vec c` be given as `a_1 hat i + a_2 hat j + a_3 hat k, b_1 hat i + b_2 hat j + b_3 hat k and c_1 hat i + c_2 hat j + c_3 hat k`, then show that `vec a xx(vec b + vec c) = vec a xx vec b + vec a xx vec c`.

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

Compute [vec a vec b vec c] where vec a = hat i- 2 hat j + 3 hat k, vec b= 2 hat i + hat j - hat k and vec c = hat j + hat k .

Compute vec a*(vec b xx vec c) where vec a = 2 hat i+ hat j + 3 hat k, vec b= - hat i +2 hat j + hat k and vec c = 3 hat i +hat j +2 hat k .

If vec a = hat i +2 hat j +hat k, vec b= 3 hat i +2 hat j- 7hat k and vec c = 5 hat i +6 hat j -5hat k . show that vec a, vec b and vec c are coplanar.

If vec a = -2hat i -2 hat j + 4 hat k, vec b=-2 hat i +4 hat j- 2 hat k and vec c = 4hat i -2 hat j -2hat k . prove that vec a, vec b, vec c are coplanar

If vec a =2 hat i + 2 hat j +3 hat k, vec b=-hat i + 2 hat j +hat k then vec a + vec b is

if vec a = 2 hat i - hat j+ hat k, vec b =hat i+ hat j - 2 hat k and vec c =hat i+ 3hat j - hat k , find λ such that vec a is perpendicular to λ vec b+ vec c

If vec a= 2 hat i+ hat j- hat k , vec b= -hat i+ 2 hat j- 4 hat k and vec c= hat i+ hat j+ hat k , find (vec a * vec b)* (vec a* vec c) .

If vec a=5 hat i-hat j-3 hat k and vec b=hat i+3 hat j -5 hat k , then show that the vecctors vec a+vec b and vec a-vec b are perpendicular.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find λ and μ if (2 hat i + 6 hat j+27 hat k) xx (hat i +λ hat j +μ hat...

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  2. Given that vec a* vec b=0 and vec a xx vec b= vec 0. What can you conc...

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  3. Let the vectors vec a, vec b, vec c be given as a1 hat i + a2 hat j +...

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  4. If either vec a = vec 0 or vec b = vec0, then vec a xx vecb = vec 0. I...

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  5. Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) a...

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  6. Find the area of the parallelogram whose adjacent sides are determined...

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

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

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

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

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

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

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

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

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

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

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

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

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