Find Parametric efuatins for the lines - The line through (1-2-2) Paralle tothe(Z)-axis.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: The plane passes through the point (18, -16, 9) and contains the line given by = = z . 1.

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Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: 3. The plane in ' with equation 4x=34 %3D

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Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

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: What is the y-coordinate of any point in the xz-plane?

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Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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Q: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

Q: Find parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

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Q: The plane with equation:

A: Given, the plane with equation:                        r→=(1, 2, 3)+m(1, 2, 5)+n(1, -1, 3)…

Q: 2. Find an equation of the plane parallel to the line

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Q: Find the distance from the point (- 11, 14, – 8) to the given plane or axis frequired, round your…

A: Given that: A point (-11, 14, -8)     NOTE: As per our answering guidelines, we can only answer 1…

Q: find the distance from the point to the plane. (2, -3, 4), x + 2y + 2z = 13

A: Given:

Q: Write an expression for the length of a parametriccurve

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Q: Determine the general equation of the plane containing the point (1, 2, –1) and the line

A: The given equation of the line- 1-x3=y+23=z-3 It can also be written as follows- x-1-3=y+23=z-31…

Q: Which point is closest to the yz-plane? ? What is the distance from the yz-plane to this point?

A: The distance of a point from the yz-plane is given by the x coordinate of the point. Because, the x…

Q: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

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Q: Find the distance from the point (3, -4, 2) to the yz-plane

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

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Q: if (u, v) and (s, t) are two distinct points in the plane, what is the distance between them?…

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Q: the coordinate plane be

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Q: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: Find the plane determined by the intersecting lines.

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Q: Find the point of intersection of the line with equation (1,8,3) + t(1,-1,3) and this plane. What is…

A: Now we will find the point of intersection.  And we  will find the y coordinate of this point

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: the distance between point and our plane is (-3, 3, -2) and not (-3, -3, -2)?

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Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: the plane whose intercepts with X zagy = b,Z=C show that the Coordinate axes are has equation Ą + +…

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Q: Find parametric equations for the lines in The line through (1, 1, 1) parallel to the z-axis

A: Given: 1,1,1 parallel to z-axis

Q: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: What is the y-coordinate of all points in the xz-plane?

A: Plane: The y-coordinate of all points in the xz plane , i.e. we need to put y=0.

Q: B. Show that line -- is parallel to plane x-2y+z = 6

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Q: Show that the plane whose intercepts with the coordinates axis are x = a, y =b, z c has equation :…

A: Consider an equation of plane as It is given that the intercepts of plane are x=a,y=b and z=c. So,…

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

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Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: Find the distance of the point (3,8,2) from the line =22= measured parallel to the plane 3x + 2y- 2z…

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Q: Find the distance from the point to the plane. (6, 0, —6), т — у %3D 4

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Q: Does the line given by x = 9 + 21t, y = - 7, z = 12 - 11t intersect the xz - ?plane yes No

A: As per bartleby guidelines we only give first one question answer.

Q: Find the distance from the point (-2, 1, 4) to the plane y = -5

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

Q: Do two intersecting lines determine a plane?

A: Two lines intersect at only one point.

Q: Find the distance between points A(1,1,0) and B(1,0,1)?

A: A1, 1, 0 & B1, 0, 1.

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…

Q: Are the plane 2x-y-4z 10 and the line {x = 2+4t,y 5- 2t,z =-8t} parallel or orthogonal?

A: We have to find out

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.