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The unit vector bisecting vec(OY) and ve...

The unit vector bisecting `vec(OY)` and `vec(OZ)` is

A

`(hati+hatj+hatk)/(sqrt(3))`

B

`(hatj-hatk)/(sqrt(2))`

C

`(hatj+hatk)/(sqrt(2))`

D

`(-hatj+hatk)/(sqrt(2))`.

Text Solution

Verified by Experts

The correct Answer is:
C
`hatj and hatk` are unit vectors along Y and Z-axes, then unit vector bisecting OY and OZ is `(hatj+hatk)/(sqrt(2))`.
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ARIHANT MATHS ENGLISH-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + v...

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

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

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

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  5. If D, E and F be the middle points of the sides BC,CA and AB of the De...

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

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

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

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

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

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  11. The sides of a parallelogram are 2hati +4hatj -5hatk and hati + 2hatj ...

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

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  13. Consider the regular hexagon ABCDEF with centre at O (origin). Q. AD...

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  14. ABCDE is a pentagon. Forces AB,AE,DC and ED act at a point. Which forc...

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

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  16. Let us define the length of a vector ahati+bhatj+chatk and |a|+|b|+|c|...

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

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

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

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

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