In Problems 39 and 40, show that the given lines intersect and find the acute angle between
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- Refer to Figure 50-22 and identify each of the following as parallel, perpendicular, or oblique lines. a. Line AB and line CD b. Line AB and EF c. Line CD and GHarrow_forward4. Find the equation of line 4 that is parallel to v=-i+3 j+ 2k and goes through the point (-6, 20,1). Hence, determine if the line 4 and L, : x= 5+ 2s, y = -9– 4.s, z = 1+7s intersect or not. If intersects, find the angle between these two lines.arrow_forwardQuestion 8 Consider the line 24x + 20y = 12 What is the y-intercept of the parallel line through (20,12)arrow_forward
- . For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line 7=(2,-1,-2) + t(3,1, -2) coplanar?arrow_forward(3) Let I be a line and P be a point not on I. Construct lines l, and l2 through P such that l, meets I at 45° and l2 meets at l at 30°. (You can use the sum of the angles inside a triangle is 180° in this problem.)arrow_forward2. At what point on the line y = b does the line segment from (0,O) to (a.0) subtend the greatest anglearrow_forward
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- 27. One line passes through the points (1, 9) and (2, 6), another line passes through (3, 3) and (-1, 5). The acute angle between the two lines is: А. 30° B. 45° С. 60° D. 135° 28. The two straight lines 4x -y +3 = 0 and 8x – 2y + 6 = 0 A. Intersects at the origin C. Are parallel D. Are perpendicular B. Are coincident 29. A line which passes through (5, 6) and (-3. -4) has an equation of A. 5x + 4y + 1 = 0 C. 5x - 4y + 1 = 0 B. 5x - 4y - 1 = 0 D. 5x + y 1 = 0 30. Find the equation of the line with slope of 2 and y-intercept of -3. В. у %3D 2х -3 А. у = -3x + 2 C. y = 2/3 x + 1 D. y = 3x - 2 31. What is the equation of the line that passes through (4, 0) and is parallel to the line x - y - 2 = 0? B. y - x + 4 = 0 D. y + x - 4 0 A. y + x + 4 = 0 C. y - x - 4 = 0 32. Determine B such that 3x + 2y - 7 = 0 is perpendicular to 2x - By + 2 = 0 А. 2 В. 3 С.4 D. 5 33. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is: A. 2x - 3y = 12 C. 3x - 2y = 12 D. 2x -…arrow_forwardTheorem 1-1 states that two lines intersect in exactly onepoint. The diagram suggests what would happen if youtried to show two "lines" drawn through two points.arrow_forward4. Evaluate , (Z - 4) dz, where r is a contour from the two line segments, the first from z = -3 to z = 4i and the second from z = 4i to z = 3+ i. Reply...arrow_forward
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