Page 253 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Note A calculator is needed. Figure Ex-45 ,, to the nearest degree.
and the line
Find the acute angle between the plane
46.

Hint See Exercise 45.

What do the lines and have in common? Explain.
47.

What is the relationship between the line , , ? and the plane
48. ? Explain your reasoning. and ,

Let and be vectors from the origin to the points
49. respectively. What does the equation

represent geometrically? Explain your reasoning. .

Write parametric equations for two perpendicular lines through the point
50.

How can you tell whether the line in 3-space is parallel to the plane
51. ?

Indicate whether the statement is true (T) or false (F). Justify your answer.
52.

(a) If a, b, and c are not all zero, then the line , , is perpendicular to the

plane .

(b) Two nonparallel lines in 3-space must intersect in at least one point.

(c) If u, v, and w are vectors in 3-space such that , then the three vectors lie in
some plane.

(d) The equation represents a line for every vector v in 2-space.

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