Using three vectors a, b, and c from the sample problem in the photo, obtain the
ID: 1397053 • Letter: U
Question
Using three vectors a, b, and c from the sample problem in the photo, obtain the following:
a. 3a - 2.5c
b.absolute value (2b + 5a)
c. angle between 3.2c - 1.7b and the y axis
Adding vectors, unit-vector components Figure 3-17a shows the following three vectors: a (4.2-(1.5 m).. F-(-1.6 m), (2.9 m c' = (-3.7m).. We can add the three vectors by components, axis by axis, and then combine the components to write the vector sum r. and culations For the x axis, we add the x componcnts of a, b, and to get the x component of the vector sum r: What is their vector sum r which is also shown? = 4.2 m . 1.6 m () 2.6 m. To add these vectors, find their net x component Similarly. for the y axis, and their nel y component. -1.5 m 2.9 m-3.7 m =-2.3 m. 3-1 We then combine thesc componcnts of to write the vector in unit vector notation: -1 -2 = (2.6 m)1-(2.3 m), (Answer) Then arrange lhe net components head lo tail. where (2.6 im)i is the vector component of 7 along the x axis and (2.3 m)j is that along the y axis. Figure 3-17b shows one way to arrange these vector components to form . (Can you sketch the other way?) s 2.6i We can also answer the question by eiving the magnitude and an angle for F. From Eq.3-6, the magnitude is -1 r- V(2.6 m) 2.3 m) 3.5m (Answer) r=V'(2.6 m)? +(-2.3 m),3.5m -2 (Answer) and the anglc (measured from the + direction) is = tan-1 -2.3 m 1 ]--41 -41(Answer) (b)- This is the result af the addition. is the vector sum of the other three vectors. Figure 3-17 Vector where the minus sign mcans clockwise.Explanation / Answer
here,
a = 4.2 i - 1.5 j
b = -1.6 i + 2.9 j
c = -3.7 j
(a)
let A = (3a - 2.5 c)
A = 3(4.2 i - 1.5 j) - 2.5(-3.7 j)
A = (12.6 i + 7.75 j )m
(b)
let B = (2b + 5a)
B = 2(-1.6 i + 2.9 j) + 5(4.2 i - 1.5 j)
B = 17.8 i - 1.7 j
|B| = sqrt(17.8^2 + 1.7^2)
|B| = 17.89 m
absolute(2b +5a) = 17.89 m
(c)
C = 3.2c - 11.7b
C = 3.2(-3.7 j) - 1.7(-1.6 i + 2.9 j)
C = 2.72 i - 16.77 j
angle with y - axis , theta = 180 + arctan(2.72/16.77)
theta = 189.21 degree
the angle between (3.2c - 1.7b) and positive y axis is 189.21 degree
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