2. Use the given equation of a line to find a point on the line and a vector parallel to the line. (x, y, z) = (4t, 7,4 + 3t)

Q: Find the coordinates of a point P on the line and a vector v parallel to the x - 7 y + 9 = z + 4…

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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: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope…

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: Find the vector equation of the line of intersection, if it exists, for each pair of planes. a. 2x…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 2 y + 5 = z +…

A: Here the given equation of the straight line is x-28=y+57=z+7  -----(i) We have to find the…

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: A given line is described by x+2y = 4. Vector A starts at the origin and ends at point P on the line…

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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.…

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Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 7 -…

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Q: Let L be the line defined by the vector equation v = [ -1, -3 ] + t [ 1, -2 ]. Find the equation y =…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x-3y 4 + 1 2 P(x,…

A: Solution ) to find the point p (x - 3)/4 = (y + 1)/2 = z + 4  = 0 (x - 3) /4 = 0   ,   (y + 1) /2  =…

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A: Let's find.

Q: Find a vector perpendicular to the lines: 4₁: x = 3-4t y=-2-6t x = -1 + 2t y=4-t L₂: O O None of…

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Q: Find the vector equation for the line of intersection of the planes 32 + 2y :0 ánd 3* + ,0 ) +t(6, r…

A: To find the equation of line intersection of given planes.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given: (2,3,-6) Perpendicular to j vector

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 − t,   y =…

A: Given :              Vector v parallel parallel to the line x=3-t, y=-1+2t , z=-2.

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

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Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 4 -…

A: Given, The equation of the line x = 7t, y = 4-t, z = 3+9t We have to find the coordinate of the…

Q: Find the coordinates of a point P on the line and a vector v parallel to the line (x + 3)/5 = y/8 =…

A: The given equation is x+35=y8=z-36   Formula used: The symmetric equation of the lines are…

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: The plane that contains the point (3, –1, -4) and the line with equation y – 1= 3z is orthogonal to…

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Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 3t, y =…

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Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

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: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

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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: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 -…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 8 y + 3 = z +…

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Q: a) Find the distance between two skew lines L1 and L2 such that L1: 1+ 4t, y=5-4t, z=-1+5t  L2:…

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

Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 =…

A: First obtain a, where a is the distance between R0 and Q.

Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

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: Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is…

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Q: Find a vector equation of the line r through D4 and perpendicular to the line s through F4 and B1.…

A: Given,D4→ = 1i ^ + 2j^ + 3k^Equation of line passing through D4→ is:x-1a= y-2b=z-3cThe above line is…

Q: Find the vector form of the equation of the line in R2 that passes through P= (2, - 1) and is…

A: If a line is parallel to another line, then they have same slope.

Q: Find the vector and the cartesian equations of the plane containing the point î+ 2j – k and parallel…

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

A: Here, in the question three vectors are given:  w1, w2, b  L is the line defined by the vector w1 We…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 5t, y = 9 –…

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Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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