session.masteringengineering.com/problemAsset/2071829/2/Hibbler.ch2.p129.jpg
A) Determine the projected component of F along AC. Express your answer to two significant figures and include the appropriate units.
B) Express this component as a Cartesian vector. Express your answer in terms of the unit vectors i, j, and k. To denote vectors in your answers, be sure to select the 'vec' button.
C)
No figures.
did you compy and past the link above so you can see the figure/
To answer these questions, we need to analyze the given diagram and use vector projection.
A) To determine the projected component of vector F along vector AC, we can use the formula for vector projection:
Proj_AB = (A · B̂)B̂
Where A · B̂ is the dot product of vectors A and B̂, and B̂ is the unit vector in the direction of vector B.
Looking at the diagram, we can see that vector F is represented by F = 3i - 2j - 6k, and vector AC is represented by AC = -4i + 4j + 8k.
First, let's find the unit vector in the direction of AC:
AĈ = (AC / |AC|) = (-4i + 4j + 8k) / √((-4)^2 + 4^2 + 8^2) = (-4i + 4j + 8k) / 12 = (-1/3)i + (1/3)j + (2/3)k
Next, let's find the dot product of F and AĈ:
F · AĈ = (3i - 2j - 6k) · ((-1/3)i + (1/3)j + (2/3)k) = -3/3 - 2/3 - 12/3 = -17/3
Finally, let's find the projected component of F along AC:
Proj_AC = (F · AĈ)AĈ = (-17/3)((-1/3)i + (1/3)j + (2/3)k)
To express this answer to two significant figures, we can calculate the numerical value of the projection.
B) To express this component as a Cartesian vector, we can simply multiply the above result by (-17/3):
(-17/3)((-1/3)i + (1/3)j + (2/3)k) = (17/9)i - (17/9)j - (34/9)k
So the Cartesian vector component of F along AC is (17/9)i - (17/9)j - (34/9)k.
C) To denote this vector in your answer using the "vec" button, you can write it as:
vec(17/9*i - 17/9*j - 34/9*k)