Two vectors are presented as a = 2.0i + 4.5 j and b = 5.0i + 4.5j. Find the foll
ID: 1519867 • Letter: T
Question
Two vectors are presented as a = 2.0i + 4.5 j and b = 5.0i + 4.5j. Find the following. a Times b (Express your answer in vector form.) a middot b (a + b) middot b the component of a along the direction of b For a cross product, use the result of applying the distribution law as given in general notation in a middot b = ab cos phi. For a dot product, use the definition of a dot product. For (c), use the rule in normal algebra of adding the two vectors before finding the product. The component of a vector along a second vector is the product of the magnitude of the first vector and the cosine of the angle between the two vectors.Explanation / Answer
a) a X b = (2i + 4.5j) X (5i + 4.5j)
a X b = 9k - 22.5k = -13.5k
b) a . b = (2i + 4.5j) . (5i + 4.5j) = 10+20.25 = 30.25
C) a+b = (2i + 4.5j) + (5i + 4.5j) = 7i + 9j
(a+b).b= (7i+9j).(5i + 4.5j) = 35+40.5 = 75.5
d) a*cos(phi)
cos(phi) = a.b/(magnitude of a * magnitude of b) = 30.25/(sqrt(2^2+4.5^2)*sqrt(5^2+4.5^2)) = 0.913
a*cos(phi) = (2i + 4.5j)*0.913 = 1.826 i + 4.1085 j
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