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Let `P ,Q ,R` and `S` be the points on the plane with position vectors `-2i-j ,4i ,3i+3ja n d-3j+2j ,` respectively. The quadrilateral `P Q R S` must be a Parallelogram, which is neither a rhombus nor a rectangle Square Rectangle, but not a square Rhombus, but not a square

A

parallelogram, which is neither rhombus nor a rectangle

B

square

C

rectangle but not a square

D

rhombus, but not a square

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A
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MCGROW HILL PUBLICATION-VECTOR ALGEBRA-EXERCISE (Level-1 Single Correct Answer Type Questions)
  1. IF r.a = 0, r. b = 0 and r. c= 0 for some non-zero vector r. Then, the...

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  2. If the position vectors of three consecutive vertices of any parallelo...

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  3. The volume of the parallelopiped whose sides are given by overset(...

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  4. The value of abs(a times i)^(2)+abs(a times j)^(2)+abs(a times k)^(2) ...

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  5. If a, b and c are any three vectors, then a times (b times c)=(a times...

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  6. ixx(a times i)+j times(a times j)+k times(a times k) is always equal t...

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  7. The value of [a times b, b times c, c times a] is

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  8. Given vectors a = (3, -1, 5) and b = (1, 2, -3). A vector c which is p...

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  9. Area of the parallelogram on the vectors a + 3b and 3a + b if abs(a)=a...

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  10. If a=x""i+5j+7k, b=i+j-k, c=i+2j+2k are coplanar then the value of x i...

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  11. If a*(b times c)=3 then

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  12. Let a=2i+2j+k and b be another vector such that a*b=14" and "a times b...

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  13. ABCDEF is a regular hexagon with centre a the origin such that vec(AB)...

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  14. A non zero vector veca is parallel to the kine of intersection of the ...

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  15. Let P ,Q ,R and S be the points on the plane with position vectors ...

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  16. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

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  17. The edges of a parallelopiped are of unit length and are parallel to ...

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  18. If a is a non-zero real number, then prove that the vectors vecalp...

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  19. If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd, wh...

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  20. Let the unit vectors a and b be perpendicular and the unit vector c be...

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