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If O is origin annd the position vector ...

If O is origin annd the position vector fo A is `4hati+5hatj`, then unit vector parallel to OA is

A

`(4)/(sqrt(41))hati`

B

`(5)/(sqrt(41))hati`

C

`(1)/(sqrt(41))(4hati+5hatj)`

D

`(1)/(sqrt(41))(4hati-5hatj)`

Text Solution

Verified by Experts

The correct Answer is:
C
Unit vector parallel to `OA=(4hati+5hatj)/(sqrt(16+15))=(1)/(sqrt(41))(4hati+5hatj)`
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The two adjacent sides of a parallelogram are given by the vectors 2hati-4hatj+5hatk and hati-2hatj-3hatk Find a unit vector parallel to its diagonal (longer). Also find the area of parallelogram.

The two adjacent sides of a parallelogram are given by the vectors 2hati-3hatj+5hatk and hati+2hatj-3hatk Find a unit vector parallel to its diagonal (longer). Also find the area of parallelogram.

The two adjacent sides of a parallelogram are given by the vectors 3hati-6hatj+hatk and hati+4hatj+3hatk Find a unit vector parallel to its diagonal (longer). Also find the area of parallelogram.

Find the vector equation of a line passing through a point with position vector 2hati-hatj+hatk and parallel t the line joining the points with position vectors -hati+4hatj+hatk and hati+2hatj+2hatk . Also, find the cartesian equivalent of the equation.

Find the vector equation of a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

If the position vector of one end of the line segment AB be 2hati+3hatj-hatk and the position vector of its middle point be 3(hati+hatj+hatk) , then find the position vector of the other end.

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ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. If a=(2,5) and b=(1,4), then vector parallel to (a+b) is

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  2. In the DeltaABC,AB=a,AC=c and BC=b, then

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  3. If O is origin annd the position vector fo A is 4hati+5hatj, then unit...

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  4. The position vectors of the points A,B and C are hati+2hatj-hatk,hati+...

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  5. The position vectors of P and Q are 5hati+4hatj+ahatk and -hati+2hatj-...

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  6. If position vector of points A,B and C are respectively hati,hatj, and...

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  7. The position vectors of A and B are 2hati-9hatj-4hatk and 6hati-3hatj+...

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  8. If the position vectors of P and Q are (hati+3hatj-7hatk) and (5hati-2...

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  9. If the position vectors of P and Q are hati+2hatj-7hatk and 5hati-2hat...

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  10. If the position vectors of A and B are hati+3hatj-7hatk and 5hati-2hat...

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  11. The direction cosines of vector a=3hati+4hatj+5hatk in the direction o...

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  12. The direction cosines of the vector 3hati-4hatj+5hatk are

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  13. The point having position vectors 2hati+3hatj+4hatk,3hati+4hatj+2hatk ...

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  14. If the position vectors of the vertices A,B and C of a DeltaABC are 7h...

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  15. If a,b and c are the position vectors of the vertices A,B and C of the...

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  16. If a and b are position vector of two points A,B and C divides AB in r...

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  17. Find the position vector of the point which divides the join of the po...

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  18. If O is origin and C is the mid - point of A (2, -1) and B ( -4, 3) . ...

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  19. If the position vectors of the points A and B are hati+3hatj-hatk and ...

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  20. The position vectors of A and B are hati-hatj+2hatk and 3hati-hatj+3ha...

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