4.4. Suppose that u = (1,3) and v = (3, 1). %3D (a) Sketch the points ļu + žv, ļu + ļv, and u + tv. (b) Draw the line of all linear combinations cu + dv with e + d = 1. (c) Sketch ļu+ jv and u+žv. Draw the line of all linear combinations си + св.

Q: 3. 6. (7, 4) and (-14, –5) 7. (5,-5) and (-5, 5) 8. (-2, 8) and (2, -10) 9. (-100, 30) and (45, -90)…

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Q: Find the cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

Q: Which of the following is the line that passes through (7,7) and is parallel to -4x-9y=-37…

A: The slopes of parallel lines are equal. We first write the given equation of line in slope intercept…

Q: Find the distance between the line L, that goes through the points A(1, 0, -1) and B(2,0, -1) and…

A: The line L1 passes through A(1,0,-1), and B(2,0,-1). the line L2 passes through C(3,1,-1), and…

Q: C. Neither par For numbers 16 - 18. Line 1:A (0, -1), B(2, -4) Line 2: C(3,5) D(-3,1) 16. The slope…

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Q: 1) Explain the four possible relationships between two lines in R. y+2 x+1 y+9 -14 z-4 2) Determine…

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Q: If A is (1, -5) and B is (9, 11), find the point that is % of the way from A to B. О а. (-5, 6) O b.…

A: We have A=1,-5, B=9,11 Now, we need to find a point which is 3/4 of the way from A to B We see that…

Q: If A is (1, -5) and B is (9, 11), find the point that is % of the way from A to B.

A: If the line segment XY¯ with coordinates Xx1,y1 and Yx2,y2 divide the segment in the ratio a:b at a…

Q: 8. A(-4, 7), B(-2, 6). C(2, -2), D(-8, 3) m(AB) m(CD) Types of Lines

A: Given that:A(-4, 7), B(-2, 6), C(2,-2) , D(-8, 3)     NOTE: As per our answering guidelines, we can…

Q: Show that the point (5,4,2), (6,2,-1) and (8,-2,-7) are collinear

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Q: Which 2 points are on the line (x,y) = (3,7) + k(-1,2), k E R Select one: (-1, 2), (3, 7) (3,7), (2,…

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Q: 4. A right triangle has vertices (-2,5), (-2,–3) and (4,-3). Find its area and perimeter. does -8 .7…

A: Given : Triangle of co-ordinates (-2,5) , (-2,-3) and (4,-3)Side length of triangle:a=8   b=6   so…

Q: 4. Line m passes through the point (2, 3) and has a slope of -. What is the equation of Line m in…

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Q: The coordinates of the missing point are A. (4, 4) В. (5, 4) (-1,4) (?, ?) С. (6, 4) D. (7, 4) x+ 3…

A: topic- sketch of a figure distance between x=3 and (-1,4) is 3-(-1)=3+1=4 x-coordinates of missing…

Q: 32. (3, 5) reflected through the y-axis is a. (-3, 5) b. (3, 5) с. (3, —5) d. (-3,-5)

A: The point of reflection is the reflected point that we get in the coordinate plane when any axis act…

Q: 7. Find the equation of the line joining the points (5, 9) and (-4, -6)

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Q: Determine the new order pairs if the points are reflected across the y- axis. J(2, 2), K(7, 4), L(9,…

A: Given- J2,2,K7,4,L9,-2 and M3,-1 To determine-  The new order pairs if the points are the reflected…

Q: 3. the dot product of -

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Q: List the intercept and test for symmetry.

A: Definition used -                x-intercept - x-intercept can be found by substituting y =0 and…

Q: 2- The line perpendicular to the triangular (PQR) and through the point (P) if P(1,-1,2), Q(0,3,1),…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.