A line, in R³ which passes through the point (xo, yo, zo) and with the direction vector (a, b, c), Select one or more: may intersect the yz-plane at (to, yo - bxo, zo — xo). - may intersect the yz-plane at (0, yo zo - 20). a - xo a may never intersect the yz-plane. may intersect the yz-plane at (0, yo - //xo, zo — xo). - may intersect the yz-plane at (-0, yo+bxo, zo + xo). Yo a a

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: Using the dot product equal to zero for perpendicular to the vectors.

Q: Prove that the equation 2x²+3xy - 2y-x+3y -1= 0 represents a pair of perpendicular lines.

A: Given that: 2x2+3xy-2y2-x+3y-1=0

Q: 1. Given three points A(1,-2), B(2,-1), and C(0,3). Determine: a. Equation of the line through A and…

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Q: e. (-27,0,2)

A: Equation of the line is x-325=y-65 and z=2

Q: 3- Find an equation of the Plane perpendicular to the line through (2,2,-9) and (7,-1,3) and…

A: To Find: Equation of plane perpendicular to the line through the points (2,2,-9) and (7,-1,3) and…

Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: 1. Determine whether the points A(3,4,-1) and B(1,-1,0) lie on the line with vector equation…

A: Given vector equation :

Q: plot the given pair on a cartesian plane {(1,1),(2,4),(3,7),(4,10),(5,13)}

A: The given pair of points are  A(1,1), B(2,4), C(3,7), D(4,10), E(5,13)

Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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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: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: Write a vector equation for the line segment from (-3, 0, 0) to (0, 4, 3).

A: To write a vector equation for the line segment from -3, 0, 0 to 0, 4, 3. To write a vector equation…

Q: Consider the lines r(t) = (2-3, +4--1) and r(s) (+4,- +3,3+6). A. Show that these two lines…

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