5) If the eastward component o
5) If the eastward component of vector is equal to the westwardcomponent of vector and their northward components are equal. Whichone of the following statements about these two vectors iscorrect?
1) Vector is parallel to vector
. 2) Vectors and point in opposite directions
. 3) Vector is perpendicular to vector
. 4) The magnitude of vector is equal to the magnitude of vector.
5) The magnitude of vector is twice the magnitude of vector.
Answer:
Let the 2 vectors be 
and 
. They can be written component wise in the cartesian coordinatesas,
We now generalise the directions in the catesian plane asfollows:
Eastward is positive X, Westward is negative X, Northward ispositive Y and Southward is negative Y.
Given
1. “Eastward component of vector is equal to the westwardcomponent of vector” this means 
2. “Northward components are equal” this means 
Now writing in terms of 
as
and we already have
- Option (1) is incorrect as these vectors arenot parallel to each other.
- Option (2) is incorrect as these vectors maypoint in same direction for
. The vectors will be 
and they both point in same direction. - Option (3) is incorrect because if we take thedot product of these vectors we have
this is zero only if 
so in general the dot product is not always zero, hence they arenot perpendicular. - Option (4) is correct as the magnitude ofthese vectors are equal(by substituting the giveninformation)
- Option (5) is incorrect as we already provedthat
. The vectors will be 
and they both point in same direction.
this is zero only if 
so in general the dot product is not always zero, hence they arenot perpendicular.
So the correct statement regarding the two given vectors is :(4) The magnitude of vector is equal to the magnitude ofvector .
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