Find the horizontal and vertical components of the vector wi

Find the horizontal and vertical components of the vector with the given length and direction, and write the vector in terms of the vectors i and j. |v| = 28, theta = 30 degree v = Find 3u, -2v, u + v, and 2u - v for the given vectors u and v. (Simplify your answers completely.) u = I + j, v = i - j 3u = -2v = u + v = 2u - 4v =

Solution

|v| = 28
theta = 30

So, horizontal component = 28cos(30)
= 28* sqrt3/2
= 14sqrt(3)

Vertical component = 28sin(30)
= 28 * 1/2
= 14

So, the vector is
<14sqrt3 , 14>

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u = i + j
v = i - j

3u = 3(i+j) = 3i + 3j --> ANS

-2v = -2(i - j) = -2i + 2j --> ANS

u + v = (i+j) + (i-j)
= i + j + i - j
2i ---> ANS

2u - 4v
2(i+j) - 4(i-j)
2i + 2j - 4i + 4j
-2i + 6j ---> ANS