In vector form (as in Exercises 5 and 6), find an equation for the line through the point (4, – 3, 7) and with direction vector (4, 2, – 3).

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: 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: Find the vector v = PQ. P = (9,4,7) Q=(10, 7, 3)

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Q: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: What is the direction of the vector with an initial point of (3,-5) and a terminal point of (8, 6)?…

A: The initial point is (3, -5) and the terminal point is (8, 6)

Q: Given, vector a = (3, 4, -2), vector b = (2, -7, 1), and vector c = (-6, 5, 4). Evaluate |-2b x c|

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Q: If A is (3,5,0), B is (-1,-2,7), and C(6,1,3) forms a triangle. Find the vector component of CB…

A: let a,b,c are position vector of point A,B,C respectively. Therefore a=3i+5j, b=-i-2j+7k c=6i+j+3k…

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: 1 Determine a vector equation of the line passing through the points A(-2, 0, 0), and B(0, 1, –3). *…

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Q: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

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

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Q: Given vector (-2,6) and a point (3,2) a. Write a vector equation  b. Write the vector equation as…

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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: 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: Find the position vector (i.e. the direction vector) from the point P(−4,−6,3) to the point…

A: To find the position vector (i.e. the direction vector) from the point  P-4, -6, 3 to the point Q4,…

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: Point A is defined by A = (3, −2, –3). The component of the vector OA resolved in the direction of…

A: Point A is defined by A=3, -2, -3. To determine the component of the vector OA→ resolved  in the…

Q: х-2 у-4 Convert the symmetric equation of the line l: to the vector equation. 6. 7

A: Here we have to convert the symmetric equation of the line l:(x-2)/6=(y-4)/7 to the vector equation.

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…

Q: A) Let the equation y = -1. What does this equation represent in R2? What does this equation…

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Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: Consider the point P(-2,3) on the coordinate system. Describe geometrically the position vector…

A: Given point P (2,3)