9. The scalar product of the vector with a unit vector along the sum of vectors is equal the one. Find the value of
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Unit vector along
10. Find the area of the with vertices A (1, 1, 2) B (2, 3, 4) and C (1, 5, 5).
Ans: A (1, 1, 2) B(2, 3, 4) C (1, 5, 5)
OB¯¯¯¯¯¯¯¯=2i^+3j^+4k^
OC¯¯¯¯¯¯¯¯=i^+5j^+5k^
11. 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.
Ans:A (1, -2, -8), B (5, 0, -2), C (11, 3, 7)
Thus and one point B is common there fore A, B, C are collinear and B divides AC in 2:3.
12. Find a vector which is to both and and . =15
Let
An
On solving equation (i) and (i
Put x, y, z in equation (i
13. Let be three vectors such that and each one of them being to the sum of the other two, find
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14. If
Find the angel between the vectors
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15. Find the sine of the angel between the vectors.
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16. Three vectors satisfy the condition Evaluate the quantity if
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Adding (i) (ii) and (iii)
17. If with reference to the right handed system of mutually unit vectors then express in the form , where is || to and is to
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18. If be three vectors such that and find the angle between
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19. Find the area of the ||gm whose adjacent sides are represented by the vectors,
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20. Find the vector joining the points P (2, 3, 0) and Q (-1, -2, -4) directed from P to Q. Also find direction ratio and direction cosine.
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