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If vec r.vec a=vec r.vec b=vec r.vec c=...

If `vec r.vec a=vec r.vec b=vec r.vec c=0` where a, b, c are non-coplanar, then

A

coplanar with a, b, c

B

parallel to `a+b+c`

C

parallel to `b xx c+c xx a+axxb`

D

parallel to `(a xx b) xx c`

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The correct Answer is:
C
Now,l `r*a=r*b`
`implies r((a-b)=0`
Similarly, `r*(b-c)=0`
Since, r is parallel to `(a-b)xx(b-c).`
So, r is parallel to `axx b +c xx a +b xx c`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -(VECTORS ) Exercise 2 ( Topical problems )
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  6. If a=hat(i)+hat(j)+hat(k), b=hat(i)+3hat(j)+5hat(k) and c=7hat(i)+9hat...

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  7. A vector of magnitude sqrt2 coplanar with hati+hatj+2hati and hati+2ha...

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  8. The angle between the vectors a=2hati+2hatj-hatk and b=6hati-3hatj...

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  9. If a and b are unit vectors, then the greatest value of |a+b|+|a-b| is

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  10. If a, b and c are non-coplanar vectors and r is a real number, then th...

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  11. Vectors a and b are such that |a|=1,|b|=4 and a.b=2." If " c=2axxb-3b,...

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  12. Three vectors a=hati+hatj-hatk, b=-hati+2hatj+hatk and c=-hati+2hatj-h...

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  13. If a parallelogram ABCD, |AB|=a, |AD|=b and |AC|=C, then DA. AB is equ...

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  14. Let a=a(1)hati+a(3)hatk, b=b(1)hati+b(3)hatk, c=c(1)hati+c(2)hatj+c(3)...

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  15. If hatu and hatv are unit vectors and theta is the acute angle between...

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  16. If the sum of two unit vectors is a unit vector, then the magnitude of...

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  17. The three vectors a, b and c with magnitude 3, 4 and 5 respectively an...

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  18. The vectors (a,a+1, a+2)(a+3, a+4, a+5)(a+6, a+7, a+8) are coplanar fo...

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  19. If a=hati+2hatk+3hatk, b=-hati+2hatj = hatk and c=3hati+hatj, then p s...

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  20. Let a=hati+2hatj+hatk, b=hati-hatj+hatk and c=hati+hatj-hatk. A vector...

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