Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) with direction vector u.

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

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Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: 1 Y

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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: 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: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Reflect the vector (-3, 5) across the line y=x

A: The vector is (-3,5)

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

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: 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 vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

Q: Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). 1+t ,te…

A: The vector equation of the line passing through the points A(x1,y1,z1) and B(x2,y2,z2)  is given by;…

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: Find the vector in the same direction as <1, 1, 0> whose component in the direction of <2,…

A: Let  us suppose that

Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

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Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

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: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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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: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

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Q: Find the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

Q: Find two vectors j and 02 whose sum is (-3, -4), where j is parallel to (0, 5) while 02 is…

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Q: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

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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: 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: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (0, 1, 3, -1) V…

A: In  the given problem we have to find the vector v with the given length and the same direction as…

Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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

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Q: Give the vector equation of the line passing through P and Q

A: Consider the points: P=1, -2Q=3, 0

Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

Q: / Determinel the Component of the Vector at each Point (州,) {0r0),(40), (-り),(り, (ー4) ニ…

A: Explanation of the answer is as follows

Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

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Q: For the vector r (3, - 1), what is -4r? The vector - 4r = ( ).

A: Given :   Vector r =  ⟨3, -1⟩  To find : -4r ?

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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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…

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…