SOLUTION: The vectors i, j are unit vectors along the x-axis and y-axis respectively. the vectors u=-i+2j and v=3i+5j are given. A vector w has the same direction as u+2v, and has a magnitud
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-> SOLUTION: The vectors i, j are unit vectors along the x-axis and y-axis respectively. the vectors u=-i+2j and v=3i+5j are given. A vector w has the same direction as u+2v, and has a magnitud
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Question 578147: The vectors i, j are unit vectors along the x-axis and y-axis respectively. the vectors u=-i+2j and v=3i+5j are given. A vector w has the same direction as u+2v, and has a magnitude of 26. Find w in terms of i and j. Answer by dfrazzetto(283) (Show Source):
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u=-i+2j v=3i+5j
w= (-i+2j) + 2(3i+5j)
w1= -i + 2j + 6i + 10j = 5i + 12j
M(w1) = sqrt(25+144) = 13, this is exactly half the desired magnitude, thus we need to multiply w1 by 2 to get w
w = 10i 24j
CHECK:
M(w) = sqrt(100+576) = sqrt(676) = 26√
