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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- The angle between two lines La and Lb is the angle between their direction vectors a and b. In Problems 35 and 36, find the angle between the given lines.35. x = 4 - t, y = 3 + 2t, z = -2tx = 5 + 2s, y = 1 + 3s, z = 5 - 6sarrow_forwardFor what values of the parameter c is the set of vectors (1,1,c), (2,c,4), (3c+1, 3, -4) in R3 linearly independent.arrow_forwardShow that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope of the line segment representing v is the same as the slope of the given line.arrow_forward
- In Problems 23–25, use the vectors u = 2i - 3j + k andv = - i + 3j + 2k.23. Find u * v.24. Find the direction angles for u.25. Find the area of the parallelogram that has u and v asadjacent sides.arrow_forwardLet y = [ 2 3 -1] and u = [ 2 -6 -6]compute the distance d from y to the line through u and the originarrow_forwardConsider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line I with symmetric equations 16 − x = y − 18 = z + 11. - Let R be the parallelogram having line segments KM and MN as adjacent sides. Show that R is a rectangle. - Determine if the vector KM and the line l are parallel.arrow_forward
- For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?arrow_forwardThe vector equation of a line that contains the point P = (1, 2, −1) and is parallel to the line l: (x, y, z) = (t, −t, 1+t), t ∈ R corresponds to?arrow_forwardShow that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the vector v is the negative reciprocal of the slope of the given line.arrow_forward
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