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If `vec(a), vec(b), vec(c )` are three vectors such that `vec(a) + vec(b) + vec(c ) = 0` and `| vec(a) | =2, |vec(b) | =3, | vec(c ) = 5`, then the value of `vec(a). vec(b) + vec(b) . vec( c ) + vec(c ).vec(a)` is

A

0

B

1

C

38

D

`-19`

Text Solution

Verified by Experts

The correct Answer is:
D
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ICSE-VECTORS -MULTIPLE CHOICE QUESTION
  1. Unit vector perpendicular to the vectors hat(i) - hat(j) and hat(i) +...

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  2. Unit vectors perpendicular to the plane of vectors vec(a) = 2 hat(*i)...

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  3. A vector of magnitude 5 and perpendicular to hat(i) - 2 hat(j) + hat(...

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  4. The area ( in sq. units ) of a parallelogram whose adjacent sides are ...

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  5. If vec( AB) xx vec(AC) =2 hat(i)-4 hat(j) + 4 hat(k) , then area of De...

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  6. The vectors from origin to the points A and B are vec(a) = 2 hat(i) - ...

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  7. The area ( in sq. units ) of the triangle having vertices with positi...

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  8. If vec(a) , vec( b) and vec( c ) are unit vectors such that vec(a) + ...

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  9. If vec(a), vec(b), vec(c ) are three vectors such that vec(a) + vec(b)...

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  10. The value ( in cubic units ) of the parallelopiped whose coterminus ed...

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  11. If vec(a) = 2 hat(i) - 3hat(j) + 2 hat(k), vec(b)= 2hat(i)-4 hat(k) an...

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  12. If vec(a) is perpendicular to vec(b) and vec( c ),| vec(a) |=2, |vec(b...

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  13. If | vec(a) | = | vec( b) | =1 and | vec(a ) xx vec( b)| =1, then

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  14. If vec(a) = hat(i) + hat(j) + hat(k), vec(a).vec(b) =1 and vec(a) xx v...

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  15. If |vec(a) | =2, | vec(b) |=7 and vec(a) xx vec(b) = 3 hat(i) + 2hat(j...

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  16. If (vec(a) + vec(b)) | vec(b) and (vec(a) + 2 vec(b))| vec(a), then

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  17. If ABCD is a rhombus whose diagonals intersect at E, then vec(EA) + ve...

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  18. If hat(i), hat(j), hat(k) are unit vectors along three mutually perpen...

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  19. The area of a triangle formed by vertices O,A and B where vec(OA) = ha...

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  20. The vectors 3 hat(i)- hat(j) + 2 hat(k) , 2 hat(i) + hat(j) + 3 hat(k)...

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