Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у - 29 г-5 and 7 perpendicular to the two lines: 3 -16 3 8 -5

Q: 3. What value of k will make the line with symmetric equations - (1,−1,3)+s(3,2,2) p vector equation…

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Q: Add the vectors u (0, 3) and i = (- 2, – 1) graphically. Your graph should include u, v and the…

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Q: Find two vectors v, and 02 whose sum is (-5, 5, –3), where 0 is parallel to (-1, –2, 1) while Dz is…

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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: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: 3. Determine the vector equation for the line with symmetric equations*=3+22=1

A: Given: Symmetric equation of line: x-34=y+25=z-13 To find: Vector equation of line.

Q: Write down the equation of the line that passes through the points (5, -1, 2) and (3, 1, 1). Using…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

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: Reflect the vector (-3, 5) across the line y=x

A: The vector is (-3,5)

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: :) Find symmetric equations for the line that passes through the point (2, –-5, 9) and is parallel…

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Q: 1. Give the vector equation of a line perpendicular to the line L: x= 21-1, y=-31, 1 e R. Are there…

A: Given line: l:x=2t-1, y=-3t, t∈ℝ To find the other line The vector equation of the line is…

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: The intersection of the two planes given by the vector equations ()- -2 =0 r. and -4 = 3 r. is

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Q: Which of the following is a direction vector for the plane with Cartesian equation 3x -2y - 5z + 3 =…

A: To find a direction vector for the given plane. The general form of plane with cartesian equation…

Q: Find the symmetric equations of the line that passes through the point (3,6, –10) and is parallel to…

A: The line passes through a point means that the point lies on the line. The direction vector of a…

Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

Q: Find the vector equation of the line, L that passes through the points P (2, -2, 8) and Q (10, 8,…

A: Given query is to find the equation of the line passing through indicated points

Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

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Q: The line that passes through the point (4, -2,0) and parallel to the vector (1, 2, –3) has symmetric…

A: The solution is given in the next step.

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: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

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

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: Find the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: Find an equation of the plane that is parallel to the vectors and , passing through the point (3,…

A: Use given parallel vectors <1,-3,1> , <4,2,0> and passing through the point (3,0,-2)…

Q: Find a vector equation of a line passing through the point (-1, -2, 4) and perpendicular to both a =…

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Show that direction vectors of the lines 2 - 2 and L: are orthogonal.

A: The given lines are x-32=y+14=z-2-1  and x-35=y+1-2=z-32. The direction vectors of the given lines…

Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

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

Q: Give the vector equation of the line passing through P and Q

A: Consider the points: P=1, -2Q=3, 0

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: What is the equation of the vector in a Cartesian coordinate system that originates from the origin…

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Q: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

Q: Find the linear equation of the plane through the point(1,2,3) and contains the line represented by…

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Q: For the vector r (3, - 1), what is -4r? The vector - 4r = ( ).

A: Given :   Vector r =  ⟨3, -1⟩  To find : -4r ?

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

A: Questions from vector calculus.

Q: Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line…

A: The vector equation of line is

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The equation of the plane perpendicular to the vector <a, b, c> is: ax+by+cz+d=0 Therefore,…

Q: Find the component form of the vector.

A: Consider the figure: Find the component of form of a vector v.   The component form of a vector in…