Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

Q: Q2: Find the equation of the plane that pass through the point P(-1,4,2) and containing the line of…

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Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

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Q: Find the equation of the plane which passes through O and is parallel to z – (5x + 6y) = 3 x+ y + z…

A: see 2nd step.

Q: Find the midpoint M of CD M = (, ) X1+X2 Y1 %3D 21 C = (-2,-10) D = (-6,0) M = ([ ? ], [ ]) Enter…

A: Explanation of the answer is as follows

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: H.W: Find the point where the line 8 +2t, y= -2t , z= 1+t intersects the plane 3x + 2y +6z = 6

A: We have to find the point where the line x=83+2t, y=-2t, z=1+t intersects the plane 3x+2y+6z=6.

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: Q2/ Find the equation of the plane through the point (2, 4, 5) perpendicular to the line: X=5+t,…

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Q: Q3)A) Find the acute angle between the planes 2x+2y-z=3and x+2y+z=2

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Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

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: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

Q: Find the angle between the plane r+y-z=21 and the line r-13y+2%3D3-2z.

A: Angle between the plane and line

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2 - 2t meets the plane 6x + 3y – 4z = -12

A: Given line is x = 2, y = 3 + 2t z = -2-2t and the plane 6x + 3y - 4z = -12

Q: Find the equation of the plane through the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

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Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

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Q: FInd the x-intercept of the plane 2x+5y+z=10

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Q: Find an equation of the plane with x-intercept = 5, y-intercept = 8 and z-intercept = 3. O Sx + 8y +…

A: In the given question we have to find the equation of the plane such that the plane intersect at…

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

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Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

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Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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Q: Q5: Find the distance of the point (2. –2,1) from the line х-2 y-3 = z+2 2 4 3 measured parallel to…

A: we have to find the distance of the point (2,-2,1) from the line x-22=y-34=z+23 measured parallel to…

Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

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Q: Find the point (x,y) of x^2+14xy+49y^2 = 100 that is closest to the origin and lies in the first…

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Q: Find the point (x, y) of x² + 14xy+49y = 100 that is closest to the origin and lies in the first…

A: we draw a shortest straight line from origin to line, which will we perpendicular then we will find…

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

Q: y = VT, y = 2 - x and r O about the x-axis?

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Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

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Q: Find the coordinates of the point where the line F = (1+21)î + tĵ – 2tk intersects the plane 2x – y…

A: Let's find.

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

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Q: Q5: Find the distance of the point (2. –2,1) from the line x-2 y-3 z+2 %D 2 4 3 measured parallel to…

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Q: H.W: Find the point where the line y=-2t, 1+t intersects the plane 3x+2y +6z 6

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Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x…

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is…

Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: Find the point at which the line 7(t) = +t intersects the yz plane.

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Q: ) Find the equation of the plane passes through the point P(2, 2, 3) and perpendicular to the two…

A: To find the equation of the plane that passes through the point P (2, 2, 3) and perpendicular to the…

Q: Find the intersection of the line and plane: x + 3y – 4z = 18, r(t) = (-3, 2, –2) + t(-3, 2, – 1)…

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Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

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Q: he cylinder x² + y² = 2y and the plane

A: Shift cylinder at origine as centre

Q: Q3/ The distance between the plane 2x+4y-4z-22%-0 and the point(1,-2.2) will be ?

A: Basic 3d geometry problem

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

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Q: Find the point on the surface r² – 2ry + 2y² – x +y = 0 closest to the point (1, 2, –3).

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Q: :: Find the y-coordinate of the point on the plane x+ 6y + 7z = 3 that is closest to the point (-14,…

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Q: Y and V are the midpoints of the legs, TX and UW, of trapezoid TUWX. If WX = 4z + 16, VY = 10z + 16,…

A: Trapezoid Midsegment Theorem states that a line segment connecting the midpoints of the legs of the…

Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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Q: Find the equation of the plane through the origin that is parallel to the plane 4.r – 2y+ 7z +12 = 0…

A: Consider the general equation of a plane, 4x-2y+7z+12=0 the normal vector of this plane will be…