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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:
= 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 x-component of vector is 3 and the magnitude of vector is 5. What is the magnitude of the y-component of vector ?
Squaring both sides we get
The direction cosines ofare
Let= ∴ Ax = 1, Ay = 1, Az = 1
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 sin2α + sin2β + sin2γ is equal to
cos2 α + cos2 β + cos2 Y = 1
(1 - sin2 α) + (1 - sin2 β) + (1 - sin2 Y) = 1
or sin2 α + sin2 β + sin2 Y = 3 - 1 = 2