Question

Two vectors, 7 and 13 centimeters in length, form an angle of 65 degrees with each other. Find the magnitude of the resultant vector.

Options:
A. 10 cm
B. 15 cm
C. 18 cm
D. 20 cm

Answer 1

The magnitude of the resultant vector is 15 cm.

Step-by-step explanation:

To find the magnitude of the resultant vector, we can use the law of cosines. Let's call the two vectors A and B with lengths 7 cm and 13 cm respectively. The angle between these vectors is 65 degrees. According to the law of cosines, the magnitude of the resultant vector R can be calculated as:

R = sqrt(A^2 + B^2 - 2ABcos(theta))

Plugging in the values, we get:

R = sqrt((7 cm)^2 + (13 cm)^2 - 2(7 cm)(13 cm)cos(65 degrees))

Simplifying, we find that R ≈ 15 cm. Therefore, the answer is option B, 15 cm.