Question 2 Consider the point P(2,-1,-4) and the vectors a =< -2,-1,2> and 6=<-3,2,2>. (a) Find the unit vector i that has the opposite direction of a. (b) Find the Plane that passes through the point P and is orthogonal to the vector 6ü - 26. (c) Find the point, if any, at which the Line with parametric equations z=-2+t, y=1-t, intersects the Plane found in part b). z=-3t

Q: Question: 1. Find the vector equations, the parametric equations, symmetric equations of line 1.…

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Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

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Q: A line passes through the point (9,1, – 1), and is parallel to the vector 7i + 3j + 7k. Find the…

A: We find the direction cosine first. As we know that the line is parallel to 7i+3j+7k So the…

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

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Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: Find the parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

A: The parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

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Q: Question 1 ( Consider the points A(2,-1,0), B(-3, 0, -2), and C(0, 3,-1). (b) Find the parametric…

A: Since A≡(2,-1,0), B≡(-3,0,-2) and C≡(0,3,-1). So AB→=-5i+j-2k, AC→=3i+4j-k and BA→=5i-j+2k. Thus…