Sunday, November 3, 2019

Precalculus, Chapter 6, 6.3, Section 6.3, Problem 37

You need to evaluate the sum of two vectors,u+v, hence you need to perform the addition of the same versors, such that:
u = 2i + 0j
v = 0i + j
u + v = (2+0)i + (0+1)j
u + v = 2i+j
Hence, evaluating the sum u + v yields u + v = 2i+j.
You need to evaluate the difference of two vectors,u-v, hence you need to perform the subtraction of the same versors, such that:
u = 2i + 0j
v = 0i + j
u - v = (2-0)i + (0-1)j
u - v = 2i-j
Hence, evaluating the difference u - v yields u - v = 2i-j.
You need to evaluate the difference of the vectors,2u-3v, hence you need to perform first the multiplication of each vector with the indicated scalar and then you need to perform the subtraction of the same versors, such that:
u = 2i + 0j => 2u = 4i + 0j
v = 0i + j => 3v = 0i + 3j
2u - 3v = 4i + 0j - 0i - 3j => 2u - 3v = 4i - 3j
Hence, evaluating the difference 2u - 3v yields 2u - 3v = 4i - 3j.

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