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If ` vec a ,\ vec b ,\ vec c` and ` vec d` are the position vectors of points `A , B ,\ C ,\ D` such that no three of them are collinear and ` vec a+ vec c= vec b+ vec d ,\ t h e n\ A B C D` is a a. rhombus b. rectangle c. square d. parallelogram

A

rhombus

B

rectangle

C

square

D

parallelogram

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-ALGEBRA OF VECTORS-Chapter Test
  1. In a quadrilateral ABCD, vec(AB) + vec(DC) =

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  2. If ABCDE is a pentagon, then vec(AB) + vec(AE) + vec(BC) + vec(DC) +...

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  3. If ABCD is a parallelogram, then vec(AC) - vec(BD) =

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  4. In a Delta ABC, " if " vec(AB) = hati - 7hatj + hatk and vec(BC) = 3 ...

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  5. If vectors vec(AB) = -3hati+ 4hatk and vec(AC) = 5hati -2hatj+4hatk ar...

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  6. The position vectors of P and Q are respectively vec a and vec b . If ...

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  7. If the points whose position vectors are 2hati + hatj + hatk , 6hati -...

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  8. The ratio in which hati + 2 hatj + 3 hatk divides the join of -2hati ...

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  9. If OACB is a parallelogrma with vec( OC) = vec(a) and vec( AB) = vec(...

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  10. The position vectors of the points A, B, C are 2 hati + hatj - hatk , ...

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  11. If ABCDEF is regular hexagon, then AD+EB+FC is

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  12. If the points with position vectors 20 hati + p hatj , 5 hati - hat...

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  13. If the position vector of a point A is vec a + 2 vec b and vec a divi...

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  14. If vec a ,\ vec b ,\ vec c and vec d are the position vectors of p...

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  15. Let G be the centroid of Delta ABC , If vec(AB) = vec a , vec(AC) = v...

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  16. If G is the intersection of diagonals of a parallelogram A B C D and O...

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  17. The vector cos alpha cos beta hati + cos alpha sin beta hatj + sin a...

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  18. In a regular hexagon A B C D E F ,\ A vec B=a ,\ B vec C= vec b\ a n d...

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  19. If three points A, B and C have position vectors hati + x hatj + 3 ha...

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  20. If the position vectors of the vertices of a triangle of a triangle ar...

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