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What should be added in vector a=3hati+4...

What should be added in vector `a=3hati+4hatj-2hatk` to get its resultant a unit vector `hati`?

A

`-2hati-4hatj+2hatk`

B

`-2hati+4hatj-2hatk`

C

`2hati+4hatj-2hatk`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let b should be added, then `a+b=hati`
`impliesb=hati-a=hati-(3hati+4hatj-2hatk)`
`=-2hati-4hatj+2hatk`
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The unit vector which is orthogonal to the vector 3hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is (a) (2hati - 6hatj + hatk)/sqrt41 (b) (2hati-3hatj)/sqrt13 (c) (3 hatj -hatk)/sqrt10 (d) (4hati + 3hatj - 3hatk)/sqrt34

The scalar product of the vector hati+2hatj+2hatk with a unit vector along the sum of vectors 3hati-4hatj+6hatk and lambdahati-3hatj+4hatk is equal to one. Find the value of lambda .

The scalar product of the vector hati+hatj+hatk with a unit vector along the sum of vectors 2hati+4hatj-5hatk and lambdahati+2hatj+3hatk is equal to one. Find the value of lambda .

The scalar product of the vector hati+3hatj+3hatk with a unit vector along the sum of vectors hati-3hatj+4hatk and lambdahati-4hatj+5hatk is equal to one. Find the value of lambda .

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.

The scalar product of the vector veca=hati+hatj+hatk with a unit vector along the sum of vectors vecb=2hati+4hatj-5hatk and vecc=lambdahati+2hatj+3hatk is equal to one. Find the value of 'lambda' and hence find the unit vector along vecb+vecc .

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 projection of the vector 2hati+3hatj+2hatk on the vector hati+2hatj+hatk

ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk, the...

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  2. What should be added in vector a=3hati+4hatj-2hatk to get its resultan...

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  3. If a=2hati+2hatj-8hatk and b=hati+3hatj-4hatk, then the magnitude of a...

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  4. If a=2hati+5hatj and b=2hati-hatj, then the unit vector along a+b will...

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  5. Find the unit vector parallel to the resultant vector of 2hati+4hatj-5...

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  6. If a=hati+2hatj+3hatk,b=-hati+2hatj+hatk and c=3hati+hatj, then the un...

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  7. If a=(2,5) and b=(1,4), then vector parallel to (a+b) is

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

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

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

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

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

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

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

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

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

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

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

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

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

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