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(a) In unit-vector notation, what is the sum of a = (4.3 m )î + (3.4 m ) ĵ and b = ( − 13.0 m )î + (7.6 m )ĵ. What are (b) the magnitude and (c) the direction of a + b (relative to î)?​

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Answer: Hope this helps:

(a) The sum of two vectors a and b in unit-vector notation can be calculated using vector addition:

a + b = (4.3 m)î + (3.4 m)ĵ + (-13.0 m)î + (7.6 m)ĵ

= (4.3 m - 13.0 m)î + (3.4 m + 7.6 m)ĵ

= (-8.7 m)î + (11.0 m)ĵ

(b) The magnitude of a vector can be calculated using the Pythagorean theorem:

|a + b| = √((-8.7 m)² + (11.0 m)²) = 12.8 m

(c) The direction of a vector relative to î can be calculated using the tangent of the angle between the vector and the x-axis (î):

tan(θ) = |(11.0 m) / (-8.7 m)| = 1.26

θ = arctan(1.26) = 57.3°

So, the direction of the vector a + b is 57.3° relative to the x-axis (î).

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