Question

There is a vector →A, with magnitude 5 units pointing towards west and vector →B, with magnitude 3 units, pointing towards south. Using vector addition, calculate the magnitude of the resultant vector.

a) 8 units.

b) 2 units.

c) 3 units.

d) 5 units.

Answer 1

The magnitude of the resultant vector is neither of the options given but approximately 5.83 units, calculated using the Pythagorean theorem since vector A and vector B are perpendicular to each other.

Step-by-step explanation:

To calculate the magnitude of the resultant vector for vector →A, with magnitude 5 units pointing towards west, and vector →B, with magnitude 3 units pointing towards south, you will use the Pythagorean theorem. Since these two vectors are perpendicular to each other, you can treat them as sides of a right-angled triangle, where the resultant vector would be the hypotenuse.

The magnitude of the resultant vector (R) is given by the square root of the sum of the squares of the two vectors:

R = √(A² + B²)

Plugging in the values, we get:

R = √(5² + 3²) = √(25 + 9) = √(34) ≈ 5.83 units

Therefore, the magnitude of the resultant vector is neither of the options a), b), c), or d), but approximately 5.83 units.