Question

A vector X is added to vector Y = 12i - 16j. The resultant vector lies along the positive x-axis and has the same magnitude as X. What is the magnitude of X? (Note: symbols in bold type are vectors).

a) 12 units.

b) 16 units.

c) 20 units.

d) 24 units.

Answer 1

The magnitude of vector X is 12 units.

Step-by-step explanation:

To find the magnitude of the vector X, we can use the Pythagorean theorem. Since the resultant vector lies along the positive x-axis and has the same magnitude as X, we know that the resultant vector has no y-component. This means that the y-component of vector Y = 12i - 16j is cancelled out by the vector X.

Therefore, the magnitude of X can be found by taking the square root of the x-component of Y squared:

Magnitude of X = √(12^2) = 12 units.