(a) Find the unit vector that is in the same direction as the vector = 1.8i 1.3j
ID: 2023429 • Letter: #
Question
(a) Find the unit vector that is in the same direction as the vector = 1.8i 1.3j 1.5k.
(b) Find the component of the vector = 1.8 1.3 1.5 in the direction of the vector = 2.7i + 3.9j.
A direction of B =
Explanation / Answer
direction as the vector = 1.8i - 1.3j - 1.5k. Now the unit vector of any direction vector v is = v/|v| where|v| represents magnitude of v so for 1.8i - 1.3j - 1.5k. we have |v| = square root(1.8^2 +(-1.3)^2 + (-1.5)^2) =2.68 => unit vector = (1.8i - 1.3j - 1.5k)/2.68 = .67i - .485j - .56k b) component of v 1.8 - 1.3 - 1.5 in any direction r = v.r/|r| where v.r is the vector dot product |r| is the magnitude of r now r = 2.7i + 3.9j => |r| = square root (2.7^2 +3.9^2) =4.74 now component vector = (1.8i - 1.3j - 1.5k).(2.7i + 3.9j)/4.74 => 4.86i/4.74 -5.07j/4.74 = 1.02i - 1.07j
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