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Find the angles between the diagonal of a cube
and its three adjacent edges.
In other words:
find each of the 3 angles between the diagonal of a
cube and the 3 sides of the cube that meet the diagonal.
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Problem 18 from section 1.2 (pg 37)
Hint: there is an easier way than the method
sugguested by the hint in the book -
sketch 2 arbitrary vectors A and B ...
now sketch (A x B) ...
now sketch v = (A x B) x A ...
what can you say about v? ...
compare this idea
with the ideas from Informal Summary 1.5.
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Problem 46 from Chapter 1 Review (pg 79).
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Let M be a sphere of radius 1 whose center is fixed at the origin
(so that M is capable of rotating only).
Describe the points on M where the torque
of F = 2 k has the largest and the smallest magnitude.
(hint: Informal Summary 1.7).
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