Find a direction vector for the line through (4, 5, 3) and (2, – 3, – 1).

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

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Q: For what values of a and ß will the vector (a, 1, B) be orthogonal to (2, 0, 7) and (-1, 1, 2)? α =…

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Q: 4x-y+5z=0

A: If a line and a plane are perpendicular to each other then the direction vector of the line and the…

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b,…

A: Given that P , Q & R lie on a straight line. It means vectors are coplanar . since if vectors…

Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: If the vectors a=(2,5,-1) and b3(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

Q: Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b five times as…

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Q: Find the direction vector of the line joining the points (a) A(7, 6) and B(-2,5), (b) with position…

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Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: Given query is to find the point and the parallel vector.

Q: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: topic - point and vector parallel to line

Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

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Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). 7(t) =…

A: The vector equation of a line passing through any two points with position vectors a  and  b is…

Q: Given that - (1, 2, 3) and - (4. 0, – 4) find the vector where %3!

A: In this question we have to find the vector z.

Q: Which of the following is a direction vector for the line through A (3, –2) and B(1, 2)? Select one:…

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Q: Find the vector equation of the line, L that passes through the points P (2, -2, 8) and Q (10, 8,…

A: Given query is to find the equation of the line passing through indicated points

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(0, 0, 0) P2(2, -2,…

A: To find:(a) the direction of vector P1P2(b) the midpoint of line segment P1P2P1(0,0,0) and…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

Q: Given the points A: (1,6,3) and B: (2,-3,3), find the vector ü = AB %3D

A: To find- vector u.

Q: Match the vectors p, q, 7, s, and t with one of the combinations of the u and i vectors from the…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: through the point (−2,4) and is perpendicular to the line  x=[31]+t[4−5] is

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Q: Find a vector perpendicular to d = [5,–4,6] and h = [-1,3,9].

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Q: Which of the following is a direction vector for the line through А (3, — 2) and В (1, 2)? Select…

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Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,…

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

Q: Find two linearly independent vectors perpendicular to the w 41 -6- 1

A: Given: vector is v→=4-91 we have to find the two linear independent vectors perpendicular the given…

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: Find a vector equation of a line passing through the point (-1, -2, 4) and perpendicular to both a =…

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Q: Find the equation of the line that passes through the point ( 8, 8, 2) and parallel to the vector .…

A: The vector equation of the line which is passing through the point (h, k, l) and parallel to the…

Q: Show that direction vectors of the lines 2 - 2 and L: are orthogonal.

A: The given lines are x-32=y+14=z-2-1  and x-35=y+1-2=z-32. The direction vectors of the given lines…

Q: . Find the direction cosines of the vector joining the two points (4, 2, 2) and (7, 6, 14).

A: Given that: Two points are (4, 2, 2) and (7, 6, 14)

Q: Find the vector equation of the line between the points (3, -1, 2) & (1, 4, -1), then graph the…

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Q: Which of the following can be the vector equation of the line passing through the points (3,2,1) and…

A: We have to find the vector equation of the line passing through the points (3,2,1) and (5/2,1,-2).

Q: Show that direction vectors of the lines L: and are arthogonal.

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Q: Find the vector equation of the line (d) through (6, −3) and parallel to the line through (5, −1)…

A: First, we find the slope of the line  through (5, −1) and (2, 11) Direction vector is=(2, 11)-(5,…

Q: Let / be the line through the point with coordinates (-1,-2,-1) in the direction of the vector Which…

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Q: Suppose the vector x characterizing the antigenic state of an influenza virus population changes…

A: The vector in the previous influenza season is 3/2, 1

Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line…

A: The vector equation of line is

Q: Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у…

A: To find the equation of line perpendicular to the given lines first we find vector perpendicular to…