Solving Parts E & F of Math Problem: Step-by-Step Guide

[Jec]

Can someone help me how can I solve parts E and F ?

 

[haruspex]

Can someone help me how can I solve parts E and F ?

Are you sure about your answer to d)? Seems to me that the three components of $\vec r$ are roughly equal, so I would not have expected the angle to be so close to 90 degrees.
For e), you may have been shown a formula for finding the component of one vector in the direction of another. If not, try answering these two questions and comparing the answers:
If you wanted the vertical component of a force F at angle theta to the vertical, what would it be?
If you took the dot product of two vectors of magnitudes a, b, with angle theta between them, what value would you get?

 

[Jec]

Are you sure about your answer to d)? Seems to me that the three components of $\vec r$ are roughly equal, so I would not have expected the angle to be so close to 90 degrees.
For e), you may have been shown a formula for finding the component of one vector in the direction of another. If not, try answering these two questions and comparing the answers:
If you wanted the vertical component of a force F at angle theta to the vertical, what would it be?
If you took the dot product of two vectors of magnitudes a, b, with angle theta between them, what value would you get?

Uhm i tried to solve again for the angle and I got 123.06 degrees but not sure.
Should I use only dot product ? would it be (6.1)(-1)+(9.4)(2)+(-8.9)(3) only?

 

[haruspex]

Uhm i tried to solve again for the angle and I got 123.06 degrees but not sure.
Should I use only dot product ? would it be (6.1)(-1)+(9.4)(2)+(-8.9)(3) only?

123 degrees sounds more ressonable. If you want me to check it exactly please post all your working.
The answer to d) is not simply a matter of taking the dot product. Please try to answer the two questions I asked.

 

[HallsofIvy]

It is useful to know that, for any vector $a\vec{i}+ b\vec{j}+ c\vec{k}$, the components of the unit vector in that direction, $(a/d)\vec{i}+ (b/d)\vec{j}+ (c/d)\vec{k}$, where $d= \sqrt{a^2+ b^2+ c^2}$, are the "direction cosines" of the vector: a/d is the cosine of the angle between the vector and the x-axis, b/d is the cosine of the angle between the vector and the y-axis, and c/d is the cosine of the angle between the vector and the z-axis.