College

Given the vectors in component form:

\[ r = \langle 8, 4 \rangle \]
\[ s = \langle -3, -4 \rangle \]
\[ t = \langle -5, 1 \rangle \]

Perform the operations: \( 5r - 3s + 8t \).

What is the magnitude and direction angle of the resultant vector?

A. 10.8, \(\theta = 56.3^\circ\)
B. 18.4, \(\theta = 119.4^\circ\)
C. 41.0, \(\theta = 77.3^\circ\)
D. 97.6, \(\theta = 24.2^\circ\)

Answer :

9514 1404 393

Answer:

C. 41.0, θ = 77.3°

Step-by-step explanation:

The sum is ...

5(8, 4) -3(-3, -4) +8(-5, 1) = (5·8-3(-3)+8(-5), 5·4-3(-4)+8·1)

= (40+9-40, 20+12+8) = (9, 40)

The magnitude is ...

√(9² +40²) = √1681 = 41

The angle is ...

arctan(40/9) ≈ 77.3°

The resultant magnitude and direction is 41∠77.3°.

Answer:

41.0, θ = 77.3°

This is the answer Edge 2020

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