2. Determine the value of ß such that the distance between the plane \pi and the line r is constant, then calculate said distance. T: x+2y+Bz+4= 0 T: 0-0-0 t 2 2

Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

Q: Given = (8,−4,1) + t(4, 4, −2), find the point where the line intersects the plane with equation z +…

A:

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 L1 : x = 2t y = 4 – t z…

A: The equation of two lines is given as follows: L1: x=2t, y=4-t, z=3+t L2: x=2+s, y=-3+2s, z=s The…

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

A:

Q: P(-2,0, 3) perpendicular to the line x = 1 – t, y = 2 + 2t, z = 3+ 4t is 6. اخترأحد الخيارات x + 2y…

A: Let me discuss this problem in step 2:

Q: Find the distance (d) from the point (- 4, 8, 4) to the plane 2x + 5y + 4z = - 50. d =

A: image is attached

Q: Find the shortest distance between the line L1:2x + y - 3 = 0 and the plane P1:3x - 4y + 12z + 5 =…

A: The formula for the distance between a point and a plane must be used to determine the shortest…

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

A:

Q: x-1 y+3 12-z Consider the following lines defined by I,: and l2: 9. =- %D 7 x = 2t + 10, y = 5t, z…

A:

Q: 3. Write an equation of the plane that is determined by the lines given by == and ==국 -2 z-2 -3 4 -1

A:

Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: Use orthogonal projection to find the distance between the { [ ] PER} (14, 21, 35); 1=

A: Given point 14, 21, 35 and line l=r1086: r∈ℝ We have to find distance between them using orthogonal…

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: b) Find the intersection point of the line Lix-1.y-3+t, z4+2t with xz-plane.

A: Here we have given equation of line and we have to find the point of intersection of given line with…

Q: Determine a so that the line x-3/a=y+5/2=z+1/4 is parallel to the plane 2x+3y-5z=14.

A: To determine  so that the line  is parallel to the plane .

Q: Find an equation of the plane containing the line a = 3t, y = 2 – 4t, z = 1+t and parallel to…

A: We have to find the equation of the plane containing the line x=3t, y=2−4t, z=1+t and parallel to…

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

A:

Q: Find the Cartesian equation of the image of the line y = 2 under the mapping z → z 2 Sketch the…

A:

Q: Which of the following mathematical models is used to determine the distance between two points…

A: