In Cartesian space, the point form of a line is e: (x, y, z) = (2 + r, -3 + 2r, 5 – 5r). - 3. a) Find the point on the line for which r b) Does the point (6, 5, – 12) lie on line €?

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

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Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. distance

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Q: ■ Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

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Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: 04: Find the distance between the parllel lines L, and L2 where L1: x = 2 - t, y = 2t, z = 1+t L2: x…

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Q: In Exercises 29 and 30, find the distance from the point to the line. 29. (2, 2, 0); x =-t, y = t, z…

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

Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

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Q: The diagram shows the parallelogram-shaped component that attaches a car's rearview mirror to the…

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Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: Consider these lines, where s,t, E R 11: [x, y, z] = [2, 1, -4] + t[1, 3, 1] 12: [x, y, z] = [1, k,…

A: Two lines are said to be coplanar if they lies in same plane. The equation of line passing through…

Q: If a plane contains two distinct points P1 and P2 then show that it contains every point on the line…

A: From Geometry: Line can be parallel to plane, intersect the plane or lie in the plane. Only third…

Q: 3. Show that the lines L1 : x = 2+t, y= 2+3t, z = 3+t and L2:1 = 2+t, y= 3+ 4t, z = 4 + 2t…

A: L1: x =2+t , y= 2+3t , z= 3+t  L2: x =2+t , y= 3+4t , z= 3+t

Q: Given: line m is the I bisector of BJ Prove: line m contains the center of OC

A: radius congurent

Q: Consider the line which passes through the point P(3, -1, -1), and which is parallel to the line x =…

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Q: let ABCD be a reactangle.The perpendicular bisector of line segment BD intersects line AB and BC in…

A: In this rectangle ABCD the perpendicular bisector of diagonal BD is EF and EF will be AC.

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: In Cartesian space, the point form of a line is e: (x, y, 2) = (2 + r, -3 + 2r, 5 5r). a) Find the…

A: In cartesian space, the point form of a line is  l : (x, y, z) = (2+r, -3+2r, 5-5r).   a) Find the…

Q: Does the relation "is parallel to" have a a) reflexive property? (consider a line m) b) symmetric…

A: a) Every line is parallel to itself. Consider a line m which is parallel to itself. Hence, the…

Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1,√5). Find the coordinates of the point S on…

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Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: Show that the midpoint of the line segment joining the points (a, b) and (c,d) is ((a + c)/2, (b +…

A: Mid point formula is:

Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Consider the line which passes through the point P(2 -3, -4), and which is parallel to the line x =…

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Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: Find the point ( x, y) such that (1, 3) is the midpoint of the line segment connecting а. (х, у) and…

A: NOTE-Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

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Q: Draw and describe the locus of points in the plane that are equidistant from parallel lines l and m.

A: Recall the fact that locus maintain an equal distance from each lines. That is, locus must be half…

Q: Consider points A, B, C, and D, no three of which are collin- ear. Using two points at a time (such…

A: Given information: A, B, C and D are four points in which no three points are collinear.…

Q: Let A, be the center of the square inscribed in acute triangle ABC with two vertice side BC (as…

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Q: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

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Q: In triangular space it is sufficient to know two different points to find the line passing through…

A: Given statement is 'True'

Q: Show that the line joining the points P(0,1, 2) and Q(3, 4, 8) is parallel to the line joining the…

A: From the given problem:    L1:P0,1,2→x1,y1,z1Q3,4,8→x2,y2,z2   L2:R-2,32,-3→x1,y1,z1S52,6,6→x2,y2,z2…

Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

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: Sketch the locus of points equidistant from D and E is the perpendicular bisector of line DE

A: Consider the line DE which is obtained by joining two point D and E. To sketch the locus of points,…

Q: Given the planes (x, y, z) = (0,0, –3) + s(1,1,–2) + t(-2, –-1,3), and x + y + z + 6 = 0 : a) Are…

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Q: Let abcd be a rectangle. the perpendicular bisector of line segment bd intersect ab and bc in point…

A: Given that ABCD be a rectangle, the perpendicular bisector of line segment BD intersect AB and BC in…

Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Suppose the symmetric equations of lines l, and l2 are = 2 – y = z and x = -1, = respectively.

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Q: Let A be the point with coordinates (0, -3, 3) and let B be the point with coordinates (2, 0, 0).…

A: Given: A=0,-3,3B=2,0,0

Q: , in general form (x + y2 + Bx + Cy + D = 0), centered a he lines 2x + y + 10 = 0 and x - 2y - 5 = 0…

A: We have to find the equation of a circle whose center is the point of intersection of,  2x+y+10=0…

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: Show the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 – t) and (x, y, z) = (13 – 3r, 13 + 2r, 4 + 4r) are…

A: Given:- Show the lines (x, y, z) = (5 + 2t, 3+2t, 1- t) and (x, y, z)= (13-3r, 13 + 2r, 4 + 4r) are…

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Q: Prove that the lines r = (1, 2, −1) + t(2, 2, 1) and r = (−1, −2, 3) + s(4, 6, −3) intersect, and…

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Q: . Find the acute angle between the line joining A(1,2,3) and and the plane containing point…

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