Determine the relative position of the line r with respect to the π plane: r: passing through the points (1,0,0) and (−2,3,4) π:z=4 Choose an option: (   )contained (   )parallel (   )orthogonal transverse (   )Transverse non-orthogonal

Q: Determine the intersection if any between the line L₁: [x, y, z] = [3, 2, − 5] + r[0, 1, 4] and the…

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Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: 2. Determine the value of ß such that the distance between the plane \pi and the line r is constant,…

A: I have appended the formula used in solution procedure

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: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Evaluate ▼ (x² y + x y z²) ·dr where C is the line segment from ( 1, – 1,0) to (2,1,3 Select one: a.…

A: Given integral is

Q: Find the angle between the line given by ⟨x, y, z⟩ = ⟨2t, 3t, t⟩ and the y-axis exactly.

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Q: ind the equation of the tongent plane to fox,y)=x²-2xy + 2y ² slope 2 in the positive x direction…

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Q: 4. Calculate the perpendicular distance between the plane with axis intercepts P(4, 0, 0), Q(0, 3,…

A: Answer is: 0.53846153846153846 Solution is given below:

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…

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Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: 1-x 2+3 Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : = y + 1 = 3 2…

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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: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

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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: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

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