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Find the area of triangle whose vertic...

Find the area of triangle
whose vertices have position vectors `hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k) `

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Find the area of the parallelogram whose Whose diagonals are the vectors 3 hat (i) + hat (j) - 2 hat (k) and hat (i) - 3 hat (j) + 4 hat (k)

Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)

Show that the vectors a = 2 hat (i) + 3hat (j) + 6 hat (k) , b = 3 hat (i) - 6 hat (j) + 2 hat (k) and c= 6 hat (i) + 2 hat (j) - 3 hat (k) are mutually perpendicular

If the vectors x hat (i) - 4 hat (j) + 5 hat (k) , hat (i) + 2 hat (j) + hat (k) and2 hat (i) - hat (j) + hat (k) are coplanar , find the value x

In each of the following show that the given vectors are coplanar: 4 hat (i) + 2 hat (j) + hat (k) , 2 hat (i) - hat (j) + 3 hat (k) , 8 hat (i) + 7 hat (k)

Find the scalar and vector projections of 3 hat (i) - hat (j) + 4 hat (k) on 2 hat (i) + 3 hat (j) - 6 hat (k)

The vectors which determine the sides of the parallelopiped are given below : hat (i) + hat (j) + hat (k) , hat (i) + 2 hat (j) + 2 hat (k) , hat (i) - 2 hat (j) + 4 hat (k)

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab

Find the area of the parallelogram whose adjacent sides are vec (a) = 3 hat (i) - hat(j) + 4 hat (k) and vec(b) = hat (i) - hat (j) + hat (k)

CHHAYA PUBLICATION-PRODUCTS OF TWO VECTORS-Exercise 2A (Very Short aanswer type questions)
  1. Find the scalar and vector projection of vec(b) on a vec (a) where v...

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  2. Find the projection of vector (vec(b)+vec (a )) on vector vec(a) wher...

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  3. Find the projection of vector (vec(b)+vec(c )) on vector vec(a) where ...

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  4. If vec | a| = sqrt(3) , |vec(b)| = 2 and vec(a) . vec(b) = sqrt(6) ,...

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  5. Find the angle made by the vector sqrt(2) hat (i) + hat (j) + hat (k)...

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  6. Find |vec(a)-vec(b)| , if two vectors vec(a) and vec(b) are such that ...

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  7. Define the vector product of two vectors vec (a) and vec (b) . Give ...

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  8. If |vec(a)|= 3 , |vec(b)| = 4 and | vec (a) xx vec(b)|= 6 , then fin...

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  9. If vec(a) , vec(b)and vec(a) xx vec(b) are three unit vectors , find t...

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  10. If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = ...

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  11. If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = ...

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  12. If vectors vec (a) = p hat (i) + 8 hat (j) + 6 hat (k) and vec (b) = -...

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  13. If (2hat (i) + 6 hat (j) + 27 hat (k) )xx (hat (i) + 3hat (j) + p hat ...

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  14. If (2 hat (i) + 6 hat (j) + 14 hat (k)) xx ( hat (i) - lambda hat (j)...

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  15. Find the area of the parallelogram whose adjacent sides are vec (a...

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  16. Find the area of the parallelogram whose whose vertices are the poin...

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  17. Find the area of the parallelogram whose Whose diagonals are the ve...

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  18. Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat ...

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  19. Find the area of triangle whose vertices have position vectors hat (...

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  20. Find the area of the triangle whose vertices are the points (1,2,3...

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