Here are two vectors: a rightarrow = (4.0 m) - (4.0 m) and b rightarrow = (6.0 m

Question

Here are two vectors: a rightarrow = (4.0 m) - (4.0 m) and b rightarrow = (6.0 m) + (8.0 m) What are (a) the magnitude and (b) the angle (relative to i) of a rightarrow ? What are (c) the magnitude and (d) the angle of b rightarrow? What are (e) the magnitude and (f) the angle of a rigtharrow + b rightarrow; (g) the magnitude and (h) the angle of b rightarrow - a rightarrow; and (i) the magnitude and (j) the angle of a rightarrow - b rightarrow ? (State your angle as a positive number.) (k) What is the angle between the directions of b rightarrow - a rightarrow and a rightarrow - b rightarrow? Number Units Number Units Number Units Number Units Number Units Number Units Number Units Number Units Number Units Number Units Number Units

Explanation / Answer

a = 4i - 4j

b = 6i + 8j

a) |a| = 42m

b) angle of a relative to i = -45 degrees

c) |b| = 10m

d) angle of b relative to i = Tan-1 (8/6) = 53 degrees

e) |a+b| = |10 i + 4j| = 229 m

f) angle of a+b relative to i = Tan-1 (4/10) = 21.80 degrees

g) |b-a| = |2i + 12j| = 237m

h) angle of b-a relative to i = Tan-1 (12/2) = 80.54 degrees

i) |a-b| = |-2i -12j| = 237m

j) angle of a-b relative to i = Tan-1 (-12/-2) = ( 180 + 80.54 )= 260.46 degrees

k) (a-b).(b-a) = 237 * 237 cos(theta)

cos(teta) = -144/(37*4) = -0.973

theta = 166.65 degrees

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