Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

Q: Find the distance from the point P(2,1) to the line v = x + 2

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Q: The lines y = 2x + 3 and y = ax + 5 are parallelif a = _____.

A: The lines y = 2x + 3 and y = ax + 5 are parallelif a = _____.

Q: Find the point on the line y = x + 1 that is closest to the point (4, 1).

A: The given equation of the line is, y=x+1 Let the point x,x+1 is closest to the point 4,1 Using…

Q: snip

A: Consider the given line  y=x+1 The point on the line is x, x+1   The distance between two points 4,…

Q: Find x'z ds, where C is the line segment from (0,2,-3) to (6,0,-6) C

A: To find:∫Cx2z dsThe line segment is from 0, 2, -3 to 6, 0, -6

Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

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Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Find the distance from the point (3,-1, 4) to the line a = 4 – t, y = 3 + 2t, z = -5+ 3t.

A: Given: point 3,-1,4 and equation of line x=4-t, y=3+2t, z=-5+3t Formula: The distance between point…

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Find | xz ds, where C is the line segment from (0,0,-6) to (-5,5,-7)

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Q: Is it true or false that the equation the distance from the point A(1,2, 6) to the line x + y + 2z =…

A: The line is l:l:x+y+2z=62x-y+z=9 and the point is 1,2,6

Q: Find the distance from the point (1, 2, 0) to the line æ = 3t, y= 1, z= 2 – t.

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Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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Q: find the distance from the point to the line. (2, 1, -1); x = 2t, y = 1 + 2t, z = 2t

A: We have to find distance from the point 2,1,-1 to the line x=2t, y=1+2t, z=2t

Q: What can you conclude if you know that the point (p, q) lies on the line y — тх + b?

A: The given equation of the line is, y=mx+b If a point lies on the line then the point satisfies the…

Q: The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 −…

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Q: Find the point at which the line intersects the given plane.

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Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and…

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and…

Q: Find the distance from the point (1, 2, 3) to the line x=0,y=2+5t,z=3+5t

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Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: We know that the equation of a line passing through the point a and parallel to the vector b is…

Q: What can you conclude if you know that the point (p, q) lies on the line y = mx + b?

A: We have to conclude if the point p, q lies on the line y=mx+b. We know that if any point is lying on…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Find the equation for the plane through Po(3,1,9) perpendicular to the following line. x = 3 + t, y…

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Q: Find the distance from the point (2, 1, 3) to the line x = 2 + 2t, y = 1 + 6t, z = 3

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Q: Find | x²z ds, where C is the line segment C from (0,-3,2) to (-3,-2,8)

A: Given C is the line segment from (0,-3,2) to (-3,-2,8) Now write the parametric equation for C…

Q: find the distance from the point to the line. (-1, 4, 3); x = 10 + 4t, y = -3, z = 4t

A: Given  Point = P (-1, 4, 3) Equation of line : L1 :  x = 10 + 4t, y = -3, z = 4t Rewrite the…

Q: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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Q: find the distance from the point to the line. (0, 0, 12); x = 4t, y = -2t, z = 2t

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Q: The lines joining the origin to the point of intersection of the line lx+my=1 and y²=4ax are at…

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Q: 12. For the two non-parallel straight lines L:2x- 5y+ 21 = 0 and L: 3x+y+6 = 0, find the coordinates…

A: Consider the following: Line-1:  2x−5y+21=0Line-2:     3x+y+6=0 At intersection point: L1=L2…

Q: Find the value of x for which line a is parallel to line b.

A: It is given that,  line a and b are parallel lines,

Q: Find the point of the line y = 2x − 1 that is closest to the origin.

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Q: Which of r = 2 sec θ and r = 2 csc θ defines a horizontal line?

A: we have to tell which of r = 2 sec θ and r = 2 csc θ defines a horizontal line.

Q: Find the equation of the line that 2 is perpendicular to y = -x and contains the point (4,-8). %3D 3

A: If two lines are perpendicular then the product of their slopes is -1. The required line is…

Q: Find the distance from the Point to the given line X- 1+t, y- 3-2t, z-4-3t and point 6. (4,1,-2)

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Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Find the equation of the specified line. through (−5, 1) parallel to −3x − 6y = 5 Y(x)=

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Q: write down the equation of the pair of straight lines joining the origin to the points of…

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Q: Find the smallest angle between the lines 2x+y-8=0 and x+3y+4=0

A: We have to find angle between lines.

Q: Find an equation of the plane determined by the point P(1,1,3) and the line given by (x-2)/3 =…

A: Given that: x-23=y+14=z-42 and P(1, 1, 3)