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The points with position vectors 10hati+...

The points with position vectors `10hati+3hatj,12hati-5hatj and ahati+11hatj` are collinear, if a is equal to

A

`-8`

B

4

C

8

D

12

Text Solution

Verified by Experts

The correct Answer is:
C
If given be A,B and C, then `AB=k(BC)` or
`2hati-8hatj=k[(a-12)hati+16hatj]`
`implies k=-(1)/(2)`
also, `2=k(a-12)`
`implies a=8`
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
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  2. If vec a , vec b are the position vectors of the points (1,-1),(-2,m)...

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  3. The points with position vectors 10hati+3hatj,12hati-5hatj and ahati+1...

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  4. The vectors hati+2hatj+3hatk,lamdahati+4hatj+7hatk,-3hati-2hatj-5hatk ...

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  5. If the points a+b,a-b and a+kb be collinear, then k is equal to

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  6. If the position vectors of A,B,C and D are 2hati+hatj,hati-3hatj,3hat...

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  7. If the vectors 3hati+2hatj-hatk and 6hati-4xhatj+yhatk are parallel, t...

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  8. Theorem 1: If a and b are two non collinear vectors; then every vector...

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  9. Four non zero vectors will always be a. linearly dependent b. linea...

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  10. The vectors a,b and a+b are

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  11. Find the all the values of lamda such that (x,y,z)!=(0,0,0)and x(hati+...

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  12. The number of integral values of p for which (p+1) hati-3hatj+phatk, p...

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  13. The vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are the ...

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  14. In the figure, a vectors x satisfies the equation x-w=v. then, x is eq...

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  15. Vectors veca = hati+2hatj+3hatk, vec b = 2hati-hatj+hatk and vecc= 3ha...

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  16. If OP=8 and OP makes angles 45^(@) and 60^(@) with OX-axis and OY-axis...

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  17. Let a,b and c be three unit vectors such that 3a+4b+5c=0. Then which o...

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  18. If A, B, C, D and E are five coplanar points, then the value of bar(D...

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  19. If the vectors vec a and vec bare linearly independent and satisfying ...

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  20. The unit vector bisecting vec(OY) and vec(OZ) is

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