In the standard (x, y) coordinate plane, what is the length of RS given R(8, 5) and S(-1,3) ?

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

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Q: Find the point at which the line T(t) = (4, 1, 7) +t( – 5, – 7, – 4) intersects the yz plane.

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Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: Show that the planes given by y − 7z = 16 and 2y − 14z = 5 are parallel, and find the distance…

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Q: 1 2x 3y + z = 0 and 2 +t - 1 1

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Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Evaluate ∫C x ds, where C is the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).

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Q: Find the distance between the skew lines defined by L1: ri(t) = L2:r5 (s) =

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Q: Find the distance between the parallel planes. x + y + z = 1 and x + y + z = 3

A: The distance between two parallel planes is the shortest distance between their surfaces. Distance…

Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

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Q: The line x=4+2t, y=-t, z=-1-4t is parallel to the plane 3x+2y+z=7 FO

A: Direction cosine vector of the line is: L=2,-1,-4 and normal vector to the plane is N=3,2,1.

Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

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Q: Find the distance between the given parallel planes. 4x – 5y + z = 16, 8x – 10y + 2z = 3

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Q: Which of the following represents two lines that are coplanar and do not intersect?

A: We want to find the lines which are coplanar and don't intersect.

Q: 1. (x² +y² +z?) ds , where Cis straight line from (1,2,3) to (4,1,4).

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Q: Find the distance between the given skew lines: x = 4+9t, y = 5+ 3t, z = 7- 6t x= 8 – t, y = 9, z =…

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Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

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Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: Find the distance between the parallel planes – 2x + y + z = 0 and - 10x – 5y – 5z – 11 = 0. - NOTE:…

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Q: Prove that the distance between parallel planes with equations

A: Given : Two planes with equations n·x=d1 and n·x=d2

Q: Find the acute angles between the intersecting lines x = t, y = 2t, z = -t and x = 1 - t, y = 5 + t,…

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Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

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Q: Let A(x,y) be the point on the line y = x + 1 that is closest to the point B(2,0). Then the square…

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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: Find the distance between the skew lines: x = 5 + 8t, y = 1+ 6t, х— 2 — t, z = 4 – 9t z = 4+ 8t y =…

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Q: Find the distance between the given parallel planes 4x – 2y+z = 16, 8x – 4y+2z=2 3 a. 3 b. 5, 14 3…

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Q: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

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Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

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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: Show that the plances x + y – z = 1 perpendicular. and 2x – 3y + 4z = 5 are neither parallel nor

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Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: Find the acute angle (in degrees) between the planes x−4y−2z=1x-4y-2z=1 and −x+3y+z=−8-x+3y+z=-8.

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Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: and V is the dosed by the Planes x=0, y=O, ニこ

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Q: Find the distance between the skew lines: y = 1+3t, y = 9, x = 3 + 8t, z = 4 – 9t x = 5 – t, z = 4+…

A: Given equation of line L1: 3+8t   , y=1+3t   , z=4-9t L2:   x=5-t  , y=9   , z=4+8t

Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

Q: Find the distance between two skew lines x = 5+t, y = 5 + 3t, z = 4 -t and x = 2t, y =t, z=t O 1 3 '…

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Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

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Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

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Q: If p is the distance between the skew lines 4,:x=1+t, y=1+6t, z=2t Lz.x =1+2f, y=5+15f, z=-2+6t,…

A: Shortest distance between two skew lines