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Show that the points A (1, - 2, - 8), B ...

Show that the points A (1, - 2, - 8), B (5, 0,- 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find a vector of magnitude 5 units, and parallel to the resultant of t...

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

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

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

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

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  7. Let a=hat(i)+4hat(j)+2hat(k), b=3hat(i)-2hat(j)+7hat(k) and c=2hat(i)-...

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  8. The scalar product of the vectorhat i+hat j+ hatk with a unit vector a...

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  9. If vec a, vec b ,vec c are mutually perpendicular vectors of equal ma...

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  10. Prove that (vec a+vec b)* (vec a+ vec b)=|vec a|^2 +|vec b|^2, if and ...

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  11. If θ is the angle between two vectors vec a and vec b, then vec a*vec ...

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  12. Let vec a and vec b be two unit vectors and θ is the angle between the...

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  13. If (hat i, hat j, hat k) are the usual three perpendicular unit vector...

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  14. If theta is the angle between any two vectors vec(a) and vec(b), "then...

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  15. If vec a is a non-zero vector, then (1/|vec a|) vec a is a..........

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  16. If vec a, vecb are non-collinear vectors, then vec a, vecb and vec a +...

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  17. The vector veca+vecb bisects the angle between the non collinear vecto...

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  18. If vec r* vec a =0 = vec r* vec b ,where vec a and vec b are non-copla...

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  19. If vec r* vec a =0 = vec r* vec b =0 and also vec r* vec c =0 for som...

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  20. If vec a and vec b are any two vectors, then (vec a xx vec b)^2 +(vec ...

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