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cosines of v.
(a) Show that .
(b) Find cos β and cos γ.
(c) Show that .
.
(d) Show that
Figure Ex-21
Use the result in Exercise 21 to estimate, to the nearest degree, the angles that a diagonal of a box with dimensions 10 cm
22. × 15 cm × 25 cm makes with the edges of the box.
Note A calculator is needed.
Referring to Exercise 21, show that two nonzero vectors, and , in 3-space are perpendicular if and only if their
23. direction cosines satisfy
24.
(a) Find the area of the triangle with vertices A(2, 3), C(4, 7), and D( , 8).
(b) Find the coordinates of the point B such that the quadrilateral is a parallelogram. What is the area of this
parallelogram?
Show that if v is orthogonal to both and , then v is orthogonal to for all scalars and .
25.
Let u and v be nonzero vectors in 2- or 3-space, and let and . Show that the vector bisects the
26. angle between u and v.
