### Chapter #2 :Vectors : Short Q/A / C.R.Q's

Ans:No
A vector comprises its components, which are orthogonal. If just
one of them has magnitude and direction, then the resultant vector has
magnitude and direction. Example:-If A is a vector and Ax is zero and Ay is
non-zero then, A=Ax+Ay then A=0+Ay A=Ay

**Q. Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors? Give mathematical reasons for your answer.**

Ans. Yes. If the angle between these two vectors is 120
degrees than it is possible.

For example:- Consider two vector having magnitude A then

R=√A

^{2}+A^{2}+2 A.A Cosθ If R=A then A=A√2Cos^{2}θ/2
=> R=√2 A

^{2}+2 A^{2}Cosθ or 1=√2Cos^{2}θ/2
R=√2
A

^{2 }(1+ Cosθ) S.O.B.S
=> R=A√2Cos

^{2}θ/2 1/2= Cos^{2}θ /2 then θ /2 =60
Or
θ=120 Degrees

**Q. Can two vectors having different magnitudes be combined to give zero resultant? Can three vectors?**

Ans. The Resultant of two vectors having different
magnitudes can not equal to zero,If they have same magnitude and opposite
direction then their resultant will be equal to zero.

Where as
the resultant of three vectors equal to zero if they form triangle after
combination.

Then

__A__+__B__+__C__=0**Q. How is it possible that i,j and k are vectors but don’t have magnitude?**

Ans. The Unit Vectors (i , j , k ) are used to show the
direction of any vector and they don’t represent any physical quantity
therefore they have no units.

**Q. For Dot Product A.B=AB cosθ. Why cosθ?**

Ans. The Dot product is “The product of magnitude of any
vector to the magnitude of projection of
another vector”.In the mathematical formula The cosθ

**represents the projection of one vector over another along X-axis.****Q. If A x B =AB and A.B=0 then what is the angle?**

Ans. A X B =AB Sinθ
A . B =AB
Cosθ

If θ= 90
degrees If
θ= 90 degrees

Then A X B= AB (b/c
Sin90=1) Then A.B =0 (b/c Cos 90=0)

**Q. Can the magnitude of any vector will be negative?**

Ans. No the magnitude of any vector can not be negative
because magnitude is calculated by

A=√ X

^{2}+Y^{2}+Z^{2}
So after
squaring, if there is any negative sign it will be removed. hats why magnitude
will not be negative

## Comments

## Post a Comment