Given planes P₁ : 2x - 3y + 5₂-6=0 and P₂ : 2x -y - z 2 +9 =6 equation of the line of intersection @ Find an plans PI and P₂ Find am quation of the plane orthogonal to of intersection of the Planes P, and P₂ through the poin't Q (4₁ -2,5) line Find the point on the plane 1 P₂ that closest to the point R (7,3,4) is

Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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Q: Find the equation for the plane through the points Po(-2,2,2), Qo (0,2,4), and Ro(3, -2,-4). ...…

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Q: (x = t r:{y = -t (z = 1+ 4t concurrent, and if so, determine the point P common to them. Check if…

A: Let the equation of a line passes through the point x0,y0,z0 with the direction vector v→=l,m,n be…

Q: Determine whether the planes a₁x + b₁y + c₁z = ₁ and 2x + ₂y + z = d₂ are parallel, perpendicular,…

A: 6x+y-5z=4 ,-42x-7y+35z=5 a1=6,b1=1,c1=-5 a2=-42 ,b2=-7,c2=35

Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

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Q: Two planes T1 and T2 are orthogonal and intersect in the line L : (x, y, z) = (−2, −5,4) + t (−1, 5,…

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Q: (i) (ii) Determine the equation of the plane M which is perpendicular to the planes with the…

A: To find the equation of a plane perpendicular to two given planes, we can use the cross product of…

Q: 7. Let z = -3 + 5i. Plot the points z,-z,7,-ž and - in the complex plane.

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Q: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

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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: Let A:(-1, 1, –1), B:(2,0, 2), C:(4, 1, –3), and D:(-3, 1, 10) be points in R. (a) Find the angles…

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

Q: Determine the equation for the plane throught the points: (5, -5, -7) and (14, -5, -9) that is…

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Q: Find the intersection of the line and plane: 3z (2x + y) = -5, P = ( r(t) = (3,-1,0) + t (-3, -2,…

A: Given line : r(t)= (3,-1,0)+t(-3,-2,-1) Given plane : 3z-(2x+y)=-5                       2x+y-3z-5=0…

Q: 3) Find equations for the lines: h the no e. The line through (1,1,1) parallel to the z-axis. f. The…

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Q: dw. Findequatian fthe plan that Passer thraugh the originand thePaint P and parallet te the tineof…

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Q: Find an equation of the plane through the three points given: P= (0,0, 1) , Q =(-1,4,2), R=(-2,–2,…

A: We have to find the equation of a plane which passes through the following points -  P = (0,0,1) Q =…