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Show that the points A(2 hat i - hat j +...

Show that the points `A(2 hat i - hat j + hat k)`, `B(hat i - 3 hat j- 5 hat k )` and `C(3 hat i - 4 hat j- 4 hat k)` are the vertices of a right angled triangle.

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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.

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.

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 ) .

Show that the points A, B and C with position vectors, vec a= 3hat i-4 hatj -4 hat k, vec b= 2 hat i -hatj +hat k and vec c =hat i-3hat j-5 hat k , respectively, form the vertices of a right angled triangle.

Show that the vectors vec a=2 hat i- hat j+ hat k , vec b=hat i-3 hat j-5 hat k , vec c=3 hat i-4hat j-4 hat k form a right angled triangle.

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.

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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.

Prove that the four points 4 hat i +5 hat j +hat k, -(hat j+hat k) ,3 hat i+ 9 hat j +4hat k and 4(-hat i+hat j + hat k) are coplanar.

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.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. If the vertices A, B, C of a triangle ABC are (1,2,3), (-1,0,0), (0,1,...

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  2. Show that the points A(1,2,7), B(2,6,3) and C(3,10,-1) are collinear.

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  3. Show that the points A(2 hat i - hat j + hat k), B(hat i - 3 hat j- 5 ...

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  4. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  5. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  6. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  7. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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  8. Find |vec a xx vec b|, if vec a = 2hat i-5 hat j+3 hat k and vec b = h...

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  9. Find a unit vector perpendicular to each of the vectors vec a+vec b an...

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  10. If a unit vector vec a, makes angles pi/3 with hat i. pi/4 with hat j ...

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  11. Show that (a-b)xx(a+b)=2(axxb)

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

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

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

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

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

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

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

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  20. 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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