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If a unit vector vec a, makes angles pi/...

If a unit vector `vec a`, makes angles `pi/3` with `hat i`. `pi/4` with `hat j` and an acute angle `θ` with `hat k`, then find `θ` and hence the component of `vec a`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. 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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  2. Find a unit vector perpendicular to each of the vectors vec a+vec b an...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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