Let L be a line satisfying the following two conditions: ) L passes through the point (6,2,3). ii) L is perpendicular to the plane 5x+9y+5z=-3. One way to write the equation of the line L corresponds to: a) (x, y, z) = (6+ 5t, 2 + 9t, 3 + 5t), with tER. %3D b) (æ, y, z) = (7 + 5t, 4 + 9t, 6 + 5t), with tER. c) (x, Y, z) = (5 + 6t, 9 + 2t, 5 + 3t), with tER. d) (x, y, z) = (4+ 6t, 7 + 2t, 2 + 3t), with tER.

Q: Consider the points A=(2,7,-4) and B=(4,5,7) in R3, one way to write the parametric equation of the…

A: Given :- Consider the points A = (2, 7, - 4) and B = (4, 5, 7) in R³, To find:- one way to write the…

Q: 5) Find the angle between the lines. y+2 %3D z-5 2x – 3 = y + 9 = 2z + 7 & x +1 = | 2 2.

A: Putting the value of drs of line , we can get angle

Q: 8. Find the point (x. y) such that (1, 3) is the midpoint of the line segment connecting a. (x, y)…

A:

Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: Consider the two lines Lı : x = 2- 3t, y = -1+ 2t, z = and L2: r = 2+ s, y = -1- 3s, z = that…

A: We will find out the required equation of plane

Q: WHAT IS THE EQUATION OF A TAMILY Of A STRAIGT LINES WITH X Y INTERCEPIC

A: We can find the equation of family of a straight lines with x and y intercepts as below

Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel.

A: According to question,Given equation of lines,4x - 3y +12 = 08x - 6y +15 =0

Q: 9. Find the equation for the plane through Po(-2,3,9) perpendicular to the line x = -2 – t, y = -3 +…

A:

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: 4. Find the equation of line 4 that is parallel to v=-i+3j+2k and goes through the point (-6,20,1).…

A: Answer is mentioned below

Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

Q: 3) Find the distances: a. Between ₁ = (3 + t, −2+ 3t, -t) and 1₂ = (1 + 2t, t, 5+ 4t). b. Between…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

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: ) Find an equation of a line that is perpendicular to both u = and v m and contains the point (2,3,…

A:

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: II. Fill in the missing entry in each row: Equation of line m X=0 Y=X 2.) X = 2 Point P (x,y) (-2,3)…

A: