Question

5) If the eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements about these two vectors is correct?

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 1

Let the 2 vectors be and . They can be written component wise in the cartesian coordinates as,

We now generalise the directions in the catesian plane as follows:

Eastward is positive X, Westward is negative X, Northward is positive Y and Southward is negative Y.

Given

1. "Eastward component of vector is equal to the westward component 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 are not parallel to each other.
• Option (2) is incorrect as these vectors may point in same direction for . The vectors will be and they both point in same direction.
• Option (3) is incorrect because if we take the dot product of these vectors we have this is zero only if so in general the dot product is not always zero, hence they are not perpendicular.
• Option (4) is correct as the magnitude of these vectors are equal(by substituting the given information)
• Option (5) is incorrect as we already proved that

So the correct statement regarding the two given vectors is : (4) The magnitude of vector is equal to the magnitude of vector .