Consider these lines in three-space. ₁: [x, y, z]= [5, -3, 6] + [-4, 1, -2] l₂: [x, y, z] = [3, -8, -6] + s[-1, 3, 5] 3: [x, y, z]= [4, 0, -1] + v[−2, 1, 2] a) Does (-3, -1, 2) lie on line ₁? b) Determine if line ₁ intersects line 2. 1 c) Determine if line ₁ intersects line 3.

Q: Find the point of intersection of lines 1₁ and 12. 1₁:r₁ = (5 + 2t₁)i + (10 - 3t₁)j + 2t₁k 12:12 =…

A:

Q: Find the x-intercept and the y-intercept of the line b 14 3. 2. -6-5 - 43456 in.

A: x- intercept is the point at which line crosses x-axis . y- intercept is the point at which line…

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: Let l1 : (x, y, z) = (131, 89, −83) + r (42, 28, −28) where r ∈ R and l2 : (x, y, z) = (29, 21,…

A: LetandShow that the lines  and  are identical.

Q: 40. Using the following ordered pairs: A(-5, 5), B(-4, -6), C(7, 7), and D(2, -4), what is the image…

A: A detailed solution is given below.

Q: Let r₁(t) = (-7, -6, -3) + t(0, 2, -3) and r₂(s) = (5, -10,-5) + s(3, 0, -2). Find the point of…

A: We want to find the point of intersection of the given two lines.

Q: (7, -8) and w=(-4,8), Given v= find v+w. v+w=

A: We know that, A vector in form of V→=a,b is represented as V→=ai^+bj^

Q: In the diagram, A is located at (0, 0), G is located at (5, 4), and I is located at (8, 4). Find the…

A: Given points: A is (0,0) G is (5,4) I is (8,4) Let the length of AC be 2a. Therefore, AF = CF = a…

Q: Find the value of X such that and are perpendicular

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Q: Are the points (−2, 1), (1, 7), and (4, 14) on the same line? Why

A: We are given three points to check if they are linear or not. Three or more points are said to be…

Q: Given t= (8,-7) and u = (-11,-4), what is t-u?

A: