Here are two vectors: a = (6.0 m)i - (2.0 m)j and b = (5.0 m)i + (7.0 m)j. (a) W

Question

Here are two vectors: a = (6.0 m)i - (2.0 m)j and b = (5.0 m)i + (7.0 m)j. (a) What is the magnitude of a? (b) What is the angle of a(relative to i)? (c) What is the magnitude of b? (d) What is the angle of b? (e) What is the magnitude of a + b? (f) What is the angle of a + b? (g) What is the magnitude of b - a? (h) What is the angle of b - a? (i) What is the magnitude of a - b? (j) What is the angle of a - b? (k) What is the angle between the directions of b - a and a - b? The angle between the two vectors is 45

Explanation / Answer

a) |a|=sqrt(36+4)=sqrt(40)m= 6.3246 m; b) cos angle=6/sqrt(40)= 0.9487; angle= 18.4349 degress; c)|b|= 8.6; d)here i am considering angle with relative to i; angle=54.4623 deg with the i-vector; e)a+b=11i+5j; |a+b|=12.08 angle=24.4 g)b-a=-i+9j; |b-a|=sqrt(82) h)angle=96.3402; i)a-b=i-9j; |a-b|=sqrt(82) angle between a-b and b-a is 0 degrees.

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