In Exercises 21 and 22, find the equation of the line containing the given points in slope–intercept form. Then, use the technique of this section to find a vector parametrization for the same line. Finally, show that your equations are equivalent.21. P(0, 5), Q(2, −1)22. P(3, −2), Q(6, 4)

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A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: 1. What is the vector and parametric forms of the equation of the line passing through points…

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Q: 10 Find the vector equation of a line whose symmetric equations are z-1 y+3 %3D 3. -4 Express your…

A: To find the vector equation of a linewhose symmetric equations are   x-12=y+33=z-1-4.

Q: What is meant by the term translation in vectors?

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Q: 3. Find a vector equation for the line through (2, 7, −3) that is orthogonal to the plane 3x + y −4z…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-4, 8, 0),…

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Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: find an equation of the plane. The plane that passes through the point  (1, −1, 1)  and contains…

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Q: Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector…

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

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Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

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Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

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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).

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Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

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Q: 9. Explain why four vectors is R³ are always linearly dependent.

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Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: Find the sum of the given vectors. а - (5, -1), ь - (-1, 8) a +b = 4,7 Illustrate geometrically. y

A: We have

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Q: Find an equation of the plane that passes through the point P(-8, –4, 7) and has the vector n = (-2,…

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Q: Q1-)A-) Find the distance from the point (0,1,1) to the line of intersection of the planes : x + 2y…

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

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Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

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Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

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Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

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Q: Q2 / A man moved from the point (2, -2, 1) to the point (8, 3, 4). Express the displacement moved by…

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A: Questions from vector calculus.

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