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Let a,b and c be three unit vectors such...

Let a,b and c be three unit vectors such that `3a+4b+5c=0`. Then which of the following statements is true?

A

a is parallel to b

B

a is perpendicular to b

C

a is neither parallel nor perpendicular to b

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`3a+4b+5c=0`
Hence, a,b and c are coplanar.
No other conclusion can be derived from it.
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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
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  4. if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + v...

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  5. If the vectors veca and vecb are linearly independent satisfying (sqrt...

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  6. Find the slope of the normal having point (3,2) and (4,1)

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  7. A line passes through the points whose position vectors are hati+hatj-...

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  8. Find the slop of line . The Equation of line is 2x-3y=2

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  9. If P and Q are the middle points of the sides BC and CD of the paralle...

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

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

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

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

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

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

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

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

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

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

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

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