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If the figure formed by the four points ...

If the figure formed by the four points `hati+hatj-hatk,2hati+3hatj,3hati+5hatj-2hatk and hatk-hatj` is

A

rectangle

B

parallelogram

C

trapezium

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `A-=(1,1,-1),B-=(2,3,0),C-=(3,5,-2) and D-=(0,-1,1)`
So, `AB=(1,2,1),BC=(1,2,-2),CD=(-3,-6,3)`
and `DA=(1,2,-2)`
Clearly, `BC||DA` but AB in not parallel to CD.
So, it is a trapezium.
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
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  2. If P and Q are the middle points of the sides BC and CD of the paralle...

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  3. If the figure formed by the four points hati+hatj-hatk,2hati+3hatj,3ha...

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  4. A and B are two points. The position vector of A is 6b-2a. A point P ...

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  5. If three points A,B and C are collinear, whose position vectors are ha...

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  6. If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC res...

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  7. The two adjacent sides of a parallelogram are 2hati+4hatj-5hatk and ha...

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  8. If A,B and C are the vertices of a triangle with position vectors vec(...

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  9. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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  10. Find the discriminant of the quadratic equation x^2+3x+2

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  11. In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

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  12. Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3...

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  13. If a and b are two non-zero and non-collinear vectors then a+b and a-b...

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  14. If |veca+ vecb| lt | veca- vecb|, then the angle between veca and vecb...

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  15. The magnitudes of mutually perpendicular forces a,b and c are 2,10 and...

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  16. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

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  17. Find the discriminant of the quadratic equation x^2+5x+4=0 and also fi...

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  18. Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja ...

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  19. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

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  20. If vecx and vecy are two non-collinear vectors and ABC is a triangle w...

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