Question

What is the resultant of the vectors shown?

Answer 1

Option (D)

Step-by-step explanation:

To find the resultant of the vectors, you can use vector subtraction. Let's assume the vector pointing north is represented by
`\vec N`, and the vector pointing east is represented by
`\vec E`.

The vector pointing north can be represented as:

`\vec N = \big < 0, N\big >`

• where 'N' is the magnitude of the vector.

The vector pointing east can be represented as:

`\vec E = \big < E, 0\big >`

• where 'E' is the magnitude of the vector.

Now, to find the resultant vector, you simply subtract vector E from vector N:

`\Longrightarrow \text{Resultant} = \vec N - \vec E \\\\\\\\\Longrightarrow \text{Resultant} = \big < 0,N\big > - \big < E,0\big > \\\\\\\\\Longrightarrow \text{Resultant} = \big < 0-E,N-0\big > \\\\\\\\\therefore \boxed{ \text{Resultant} = \big < -E,N\big > }`

Since 'E' is negative it will point opposite of east, so west. Since 'N' is positive it will continue to point north. Thus, the resultant vector will point northwest. This makes option (D) correct.