Question

Two vectors A and B are at right angles to each other. The magnitude of A is 12 units, and the magnitude of B is 5 units. What is the magnitude of vector A plus vector B?

a) 1
b) 7
c) 5
d) 13
e) 17

Answer 1

The magnitude of the sum of two right-angle vectors, A with a magnitude of 12 units and B with a magnitude of 5 units, is found using the Pythagorean theorem, resulting in 13 units.

Step-by-step explanation:

When two vectors A and B are at right angles to each other, the magnitude of their sum can be computed using the Pythagorean theorem. The magnitude of vector A is 12 units, and the magnitude of B is 5 units. According to the theorem, the magnitude of the resultant vector, which is vector A plus vector B, can be found by taking the square root of the sum of the squares of their magnitudes:

• A = 12 units
• B = 5 units

To find the magnitude of A + B:

(Magnitude of A + B) = sqrt(A² + B²)
= sqrt(12² + 5²)
= sqrt(144 + 25)
= sqrt(169)
= 13

Therefore, the magnitude of the vector A plus vector B is 13 units.