Let v = (-3,8) and there is a line m through (2, 5). a. Write the vector equation for the line if m is parallel to V. | b. Write the parametric equation for line if m is perpendicular to v.

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Define direction vector.

A: Define direction vector.

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: 1. Given three points A(1,-2), B(2,-1), and C(0,3). Determine: a. Equation of the line through A and…

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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: Hw.L showthat Vi=3inbj andVz 2-i-zj have opfosite directions.

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Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: rite the equation of the line passing through P with direction vector d in vector form and…

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Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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Q: Write the parametric equations of the line through the point (1,2,3) parallel to the vector a =.…

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Q: What is the shortest distance d from the line L₁ defined by the vector equation to the line L₂…

A: Consider 2 lines in vector form as: v1 = a1 + c * b v2 = a2 + d * b here, c and d are the constants.…

Q: Describe the result when a point or line is changed by a vector

A: We will describe this.

Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

A: Given- A=(1,2,0) , B=(3,4,-1), C=(4,5,2) To find the exact value of distance between point C and the…

Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

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Q: Find the direction of v:v =(7,-2)

A: Given: v→=7,-2

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

A: Hint: A vector v→ is perpendicular to both a→=a1i^+a2j^+a3k^ and b→=b1i^+b2j^+b3k^ if v→=a→×b→…