Question
Vector A has a magnitude of 248 N and direction angles of α = 85°, β = 114°, and γ = 25°. Express Vector A in unit vector notation.
Answers
To find the direction cosines of the vector,
l = cos(α) = cos(85)
m = cos(β) = cos(114)
n = cos(γ) = cos(25)
Now, the unit vector can be represented as:
li + mj + nk (i, j, k, are orthogonal unit vectors)
=> Unit vector = cos(85)i + cos(114)j + cos(25)k
Vector = Magnitude * Unit Vector
= 248(cos(85)i + cos(114)j + cos(25)k)
l = cos(α) = cos(85)
m = cos(β) = cos(114)
n = cos(γ) = cos(25)
Now, the unit vector can be represented as:
li + mj + nk (i, j, k, are orthogonal unit vectors)
=> Unit vector = cos(85)i + cos(114)j + cos(25)k
Vector = Magnitude * Unit Vector
= 248(cos(85)i + cos(114)j + cos(25)k)
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