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For a vector with direction angles α = 30°, β = 45°, and γ = 60°, what is the component along the x-axis?
0
0.5
0.866
1
If the direction angles of a vector are α, β, and γ, what is the relationship between these angles?
α = β = γ
α + β + γ = 90°
α + β + γ = 180°
α + β + γ = 360°
The direction cosines of a vector are usually denoted by:
α, β, γ
L, M, N
x, y, z
l, m, n
Fill in the blanks.
The range of values for direction angles in a 3D space are ___
0° to 180°
-180° to 180°
0° to 360°
-90° to 90°
If a vector's direction cosines are l = 0.6, m = -0.8, and n = 0.3, what is the direction angle with the x-axis?
36.87°
53.13°
45°
60°
A vector is directed along the positive x-axis. Its direction angles are ____
α = 0°, β = 0°, γ = 0°
α = 90°, β = 0°, γ = 0°
α = 0°, β = 90°, γ = 0°
α = 0°, β = 0°, γ = 90°
Is this statement true or false?
In a 3D Cartesian coordinate system, a vector has 3 direction angles
True
False
If a vector lies in the xy-plane, then the value of its direction angle with the z-axis is ___
0°
90°
180°
The dot product of a vector with its direction cosines is equal to:
-1
2
Cosine trigonometric function is used to find the direction angles of a vector
It is done.