2. Use the given equation of a line to find a point on the line and a vector parallel to the line. (x, y, z) = (4t,7,4 + 3t)

Q: iven the vectors a = (3,2,-1) and b = (1, -2,3), find the equation of the line joining a nd b. Show…

A: This is a problem of 3D geometry and calculus.

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: Write down the vector equation of the line passing through the points with position vectors p=…

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Q: Determine whether the lines L₁ and L2 given by the vector equations are parallel, perpendicular, or…

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Q: et L₁ be the line passing through the points Q₁(-5, 2,-5) and Q₂(-14, -7, 1) and let L₂ be the line…

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Q: GIven vectors =(-5,9) and v = (-1, 1), find u v. %3D

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Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

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Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: he vector v = ai + bj is parallel to the line bx – ay = c. Use this fact to find ector starting at…

A: Introduction: The formula for the equation of the line passing through a point P(a,b) is given by,…

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: A point A(-5,-3) is translated by the vector v = , and then reflected about the line y=0. the…

A: Given that: A(-5, -3) is translated by v=<8, 0>

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

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

Q: find an equationfor the line through P parallel to v. Then sketch the line. Include v inyour sketch…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Consider the vestun . il 1:= V2: V3: and u where a E R. (a) For which values of a is the span(v1,…

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Q: Find the vector equation of the line that goes through the point (18, 11, 20) and is perpendicular…

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Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…