Use the result in Exercise 21 to find the equation of the line that contains (4, 5) and is perpendicular to the graph of 2x + 3y = 6.

Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

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Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

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

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

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

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Q: Find the general equation Ax + By = C for the line with slope m = y intercept - 2. - and %3D

A: Given: The slope of the line is -23. The y-intercept is -2.  Formula used: Slope intercept form. The…

Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

Q: prove that the equation 2x²+3xy-2y²-x+3y-1=0 represents a pair of perpendicular lines

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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: Prove that the equation 2x2+xy-6y2+7y-2=0 represents a pair of straight lines

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Q: Prove that the equation 2x²+3xy-2y²-x+3y-1=0 represent the pair of perpendicular line

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Q: Prove that the equation 2x²+3xy - 2y-x+3y -1= 0 represents a pair of perpendicular lines.

A: Given that: 2x2+3xy-2y2-x+3y-1=0

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

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: Use the given condition to write an equation for the line in slope-intercept form. Passing through…

A: It is given that the line passes through (5,4) and is perpendicular to the line

Q: Find equation of the plane that contains the lines L,:x 3+5t, y = 6+2t, z = 7t and L2: x = 7t, y =…

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Q: Find the stope intercept equation of a line that has y hntercept of 4 and is parallel to the line 5x…

A: Given query is to find the equation of the indicated line.

Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: Find the equation of the line that intersects the lines 2x + y – 1= 0 = x – 2y + 3z 3x – y + z + 2 =…

A: We have to find the equation of the line that intersects the given lines and parallel to the line…

Q: Write an equation of the line containing the given point and parallel to the given line.  Express in…

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Q: Prove that the equation 2x²-3xy-2y²-x+3y-1=0 represents a pair of perpendicular lines

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Q: Use the result in Exercise 21 to find the equation of the line that contains (5, – 1) and is…

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Q: Prove that the equation 2x2+3xy-2y2-x+3y-1=0 represent the pair of perpendicular lines

A: To Prove that the equation 2x2+3xy-2y2-x+3y-1=0 represent the pair of perpendicular lines

Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

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Q: Find the slope intercept form of the line satisfying the given conditions. parallel to 4x+16y=23.…

A: The line parallel to the given line 4x+16y=23 should have the same slope as the given line.

Q: Use slopes to determine if the lines 2x+5y=3 and 5x+2y=-1 are perpendicular

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Q: The line joining the origin and Pomt of of the linesr (X=1+2t,42-3+4t. y=-5+3t 2 Ction ,zet) and

A: Let the parameter of line L1 is t = t1 and the parameter of line L2 is t = t2. To find the point of…

Q: E. Show that the lines 3x - 5y + 19 =0 and 10x + 6y -50 =10 are perpendicular and find their point…

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Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: find the point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

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Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: Prove that the equation 2x2+3xy-2y2-x+3y-1=0 represents a pair of perpendicular lines

A: Solution: The objective is to find whether the given equation represents a pair of perpendicular…

Q: Use slopes to verify that the graphs of the equations Ax + By = C and Bx - Ay = D are perpendicular.…

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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: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: 45. Parallel to -3x + 4y = 12, passing through (-4, – 6)

A: The line is parallel to -3x+4y=12, passing through -4,-6

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find the foot of the perpendicular drawn from (4,1) upon the straight line 3x – 4y + 12 = 0 -

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Q: 4) Find the point in which the line through the origin perpendicular to the plan 2x - y -z = 4 meets…

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Q: Find equation of the line Passes through the Peint (-3,2,-1)-and parallel te the lineof intersection…

A: Given that: The given point is: (-3, 2, -1)The planes are: π1: x+2y+z=8 and π2:x+y-z=2

Q: find the point in which the line meets the plane x = 1 + 2t, y = 1 + 5t, z = 3t; x + y + z = 2

A: Given, The equation of line x = 1 + 2t, y = 1 + 5t, z = 3t and the equation of plane is x + y + z =…

Q: Find the point (Xo, Yo) on the line 4x + 6y = 12 that is closest to the origin. (Xo, Yo) =

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Q: standard form of the line with center (5,1) and tangent to the line 7x+2y=17

A: Given Data: Center: (x1, y1) = (5, 1) Tangent: 7x+2y=17   The general equation of tangent is,…

Q: Use the result in Exercise 20 to find the equation of the line that contains (4, 5) and is parallel…

A: We know the important theorem is that the graph of Ax+By=C is parallel to the graph of Ax+By=D.…

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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Q: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…