Question

Consider the following vectors in component form a=<2,10>, b=<-5,-14>, c=a-b.

What is the magnitude and direction angle of vector c? )
a) |c|=5, θ =36.9°
b) |c|=5, θ =53.1°
c) |c|=25, θ =16.3°
d) |c|=25, θ =73.7°

Answer 1

Vector c is calculated by subtracting vector b from vector a, resulting in c=<7,24>. The magnitude of c is 25, and its direction angle is approximately 73.7°. Thus, the correct answer is option d) |c|=25, θ =73.7°.

Step-by-step explanation:

To calculate the magnitude and direction angle of vector c, we first need to find vector c by subtracting vector b from vector a. Given a=<2,10> and b=<-5,-14>, the vector c is computed as c = a - b = <2 - (-5), 10 - (-14)> = <7, 24>. The magnitude of vector c, denoted as |c|, is the square root of the sum of the squares of its components: |c| = √(7² + 24²) = √(49 + 576) = √625 = 25.

To find the direction angle θ, we use the tangent function, θ = arctan(cᵢ/cᵠ) = arctan(24/7). Upon calculating this using a calculator set to degree mode, we get θ ≈ 73.7°. Therefore, the magnitude of vector c is 25 and the direction angle is approximately 73.7°.

From the given options, d) |c|=25, θ =73.7° is the correct choice.