If C= -5j + 6j - 3k and
D= 7i + 8j + 4k are vectors, find:
The cross product and its respectively angle
I assume you mean the angle between CxD and the plane of C and D.
CxD = 48i+j-82k
Since CxD = |C||D|sinθ,
sinθ = 95.0211/(8.3666*11.3578) = .9999
θ = 89.4°
ignore my comment. the angle between C and D is found.
To find the cross product of two vectors C and D, you can use the formula:
C × D = (C₁D₂ - C₂D₁)i + (C₃D₁ - C₁D₃)j + (C₂D₃ - C₃D₂)k
Let's calculate the cross product:
C₁D₂ = (-5) * 8 = -40
C₂D₁ = (6) * 7 = 42
C₃D₁ = (-3) * 7 = -21
C₁D₃ = (-5) * 4 = -20
C₂D₃ = (6) * 4 = 24
C₃D₂ = (-3) * 8 = -24
Now substituting these values into the cross product formula:
C × D = (-40 - 42)i + (-21 + 20)j + (24 - (-24))k
= -82i - 1j + 48k
= -82i - j + 48k
The cross product of vectors C and D is -82i - j + 48k.
To find the angle between two vectors, you can use the dot product of the vectors. However, the angle between two vectors cannot be determined from the cross product alone. The dot product of two vectors can be calculated using the formula:
C · D = |C| |D| cos(θ)
Where |C| and |D| are the magnitudes of vectors C and D, respectively, and θ is the angle between the two vectors. From the given question, we know the components of vectors C and D, but we don't have the magnitudes. Therefore, we cannot calculate the angle between them without additional information.