Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are parallel and find the distance between them. NOTE: Enter the exact answer. L₁ and L₂ are parallel because they are parallel to vectors v₁ and v₂ that satisfy : Choose one D= ||

Q: 5. For the vectors = (-3, –4) and v = (-2, 2) Find the dot product u · v, and the angle 0 between…

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Q: Show that the lines L₁ : x = 1 -t, y = 2t, z = 5 + t and L₂: x=1+3t, y = 3-6t, z = 5-3t are parallel…

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Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: 02. Given the vectors : A = (3.-1, 2), B = (0, 1, 1) and C- (2, 2,-1), find: the angles between the…

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Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

A: Vector: An object which has both magnitude as well as direction is called a vector. We can draw a…

Q: Let a = (-2, 0, 5) and b = (-3,- 2, 4). Find the angle between the vectors (in degrees).

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Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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Q: Assume v₁ = [3,-2] and v₂ = [-1,4]. Find the sum and difference of vectors v₁ and v₂. V₁ + V₂ = [ ]…

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