Question

For vectors →B=−ˆi−4ˆj and →A=−3ˆi−2ˆj, calculate (a) →A+→B and its magnitude and direction angle, and (b) →A−→B and its magnitude and direction angle.

a) (a) Resultant vector: (-4i - 6j), Magnitude: 7.211, Direction angle: 120°; (b) Resultant vector: (2i + 2j), Magnitude: 2.828, Direction angle: 45°
b) (a) Resultant vector: (-4i - 6j), Magnitude: 7.211, Direction angle: 150°; (b) Resultant vector: (2i + 2j), Magnitude: 3.000, Direction angle: 60°
c) (a) Resultant vector: (-5i - 6j), Magnitude: 7.810, Direction angle: 127°; (b) Resultant vector: (1i + 2j), Magnitude: 2.236, Direction angle: 63°
d) (a) Resultant vector: (-3i - 6j), Magnitude: 6.708, Direction angle: 150°; (b) Resultant vector: (1i + 2j), Magnitude: 2.236, Direction angle: 45°

Answer 1

To find the sum of two vectors, you simply add their corresponding components. The magnitude of the sum vector is found using the Pythagorean theorem, and the direction angle can be calculated using trigonometry.

Step-by-step explanation:

To find the sum of two vectors, you simply add their corresponding components. For the vectors →B = -îi - 4ụj and →A = -3îi - 2ụj, the sum is given by (→A + →B) = (-3î - 2ụj) + (-îi - 4ụj) = (-4îi - 6ụj).

To calculate the magnitude of a vector, you can use the Pythagorean theorem. The magnitude of the sum vector is given by the formula |→C| = √(Cx2 + Cy2), where Cx and Cy are the x and y components of the vector. Plugging in the values, we get |→C| = √((-4)2 + (-6)2) = 7.211 units.

The direction angle of a vector can be calculated using the formula tan(θ) = Cy/Cx, where θ is the direction angle. Solving for θ, we get θ = tan-1(Cy/Cx). Plugging in the values, we get θ = tan-1(-6/-4) = 120°.