Find the resultant of two vectors of a unit and if unit acting art a point art an angle 45° of each other

Answer 1

To find the resultant of two vectors of unit magnitude, we can use the parallelogram law or the triangle law of vector addition.

Using the parallelogram law, we can draw two vectors starting from the same point and forming a parallelogram. The diagonal of the parallelogram is the resultant vector.

The magnitude of each vector is 1, and they are acting at an angle of 45 degrees with respect to each other. Since they are both of unit magnitude, we can consider them as the vectors (1, 0) and (0, 1) in the x-y coordinate system.

Let's name the first vector A and the second vector B.

A = (1, 0)
B = (0, 1)

Using the parallelogram law, we can create the parallelogram by copying vector B and placing the tip of it at the tip of vector A. After drawing the parallelogram, the diagonal represents the resultant vector.

To find the resultant vector, we can use the formula:

Resultant = vector A + vector B

Using vector addition, we add the corresponding components of vectors A and B:

Resultant = (1 + 0, 0 + 1)
= (1, 1)

Therefore, the resultant vector is (1, 1).

To find the magnitude of the resultant vector, we can use the Pythagorean theorem:

Magnitude of Resultant = √(x^2 + y^2)
= √(1^2 + 1^2)
= √2

Therefore, the magnitude of the resultant vector is √2.