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If n is a unit vector in the direction of the vector then
Unit vector is vector with magnitude unity but having specific direction.
Value of unit vector is given by:
Where,
= unit vector
A = vector a
∣A∣ = magnitude of vector a
The components of Vector along the directions of vectors () is
Given , (say) components of along the direction of
The magnitude of the xcomponent of vector is 3 and the magnitude of vector is 5. What is the magnitude of the ycomponent of vector ?
Squaring both sides we get
Let= ∴ A_{x} = 1, A_{y} = 1, A_{z} = 1
and
cos α, cos β andcos y are the direction cosines of .
If a vector makes angles α, β and γ with X, Y and Z axes respectively then sin^{2}α + sin^{2}β + sin^{2}γ is equal to
cos^{2} α + cos^{2} β + cos^{2} Y = 1
(1  sin^{2} α) + (1  sin^{2} β) + (1  sin^{2 }Y) = 1
or sin^{2} α + sin^{2} β + sin^{2} Y = 3  1 = 2
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