Question 3. (a) Prove that the planes 4x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the vector equation of the line of intersection.

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A: equation of line in vector parametric form

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Q1, Find Paametric equations for the line through the Point (0,1, 2) that is U =i 12}+ 3k and ū= 3i…

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Q: Find the vector, parametric, and symmetric equations of the line which passes through the points A =…

A: Given points are: A=3,1,-1 and B=7,0,1 To find the vector, parametric, and symmetric equations

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Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: we have to find

Q: Ps Fnd Parametric equations for the 3. lines through (2,3,0) Perpendliculerr to the Vector uiitzj+3k…

A: First take cross product ie normal vector And then use formula

Q: QUESTION 10 Let r(t)=(1-t2, 5t, 2t3). Find the z-component of the vector r'(4).

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Q: Question 19 Let L be the line passing through the point P-(-1, 2, 2) with direction vector d-[1,-2,…

A: First find the equation is line by given points and direction.  Then assume it T and convert (x,y,z)…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t y…

A: Given, The parametric equation of the line D passing through A and parallel to vector v is  x =…

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Q: O Find the parametric equation of the line through the point (-3,1,6) parallel to the vector V 2i +…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: If a line is parallel to the vector 4i + 1j+ 4k and passes through the point P = (3,7,9), then the…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

A:

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 parametric equations for the line through the point P(2, - 5, - 3) parallel to the vector 31 -…

A: topic - equation of a line

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: QUESTION 3 Let r(t)=(1-t?,5t,2t3). r'(3). Find the z-component of the vector

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Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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Q: Find the parametric equations of the line through the point P(1, 2, 4) and parallel to the vector .

A: use the parametric form  of line .

Q: Find the parametric equation of the line that passes through the point P(2,4, –2) and is parallel to…

A: Parametric equation of line that passes through the point P(x0, y0, z0)& parallel to vector a =…

Q: 1. Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through…

A: Parametric and vector equation of line

Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: 1. Find both the vector equation and the parametric equations of the line through (−3​,5​,6​)and…

A:

Q: Questions 1 - 5. Consider the plane that goes through the point (4, 1, 3) and is orthogonal to…

A: Given that the plane that goes through the point (4,1,3) and is orthogonal to vector (2,3,1) . Here…

Q: 4. (a) Find a parametric equation and symmetric equation of the line that pases through the point…

A: We have a point P(2,-1,3) and a vector  i^+2j^-3k^ We have to find a parametric equation and…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2 + 3t…

A:

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: QUESTION 23 Find the vector equation of the line through the point 71and perpendicular to the plane…

A: The vector equation of a plane is, a→ is the vector on the plane given and r→ is the variable vector…

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

A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

Q: Find the vector parametric equations for the line. in the direction of the vector 4 i – 3j- 3k and…

A: Equation of the line passing through a given point a,b,c and in a given direction l i+m j+n k is…

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: b) Find parametric equations of the plane (P) containing the point P(1,-2, 0) and the vectors û and…

A:

Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

Q: If a line is parallel to the vector 8i + 5j+3k and passes through the point P = (6,2, 4), then the…

A: The line which is parallel to the vector  ai + bj + ck and passes through (x1 , y1 , z1) has the…

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: Give a vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

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Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

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Q: Question 3 Determine which vector from the options below is in the plane: 1 I = S + tl 2 - TO Omo

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Q: Give a vector parametric equation for the line through the point (1,−4,1) that is parallel to the…

A: We have to find the vector parametric equation for the line through the point (1,-4,1) that is…

Q: If a line is parallel to the vector 7i + 5j+ 5k and passes through the point P=(4,3,5), then the…

A: To find the parametric equation of the line:Given line is parallel to the vector 7i+5j+5kSo, a=7,…

Q: (6) Show that the vector equations r = -2i + j+ t(-į+ 5j) and r = -3i + 6j + s(-3i + 15j) | | refer…

A: The vector equation of a line is r⇀=a⇀+λb⇀. Where a⇀ and b⇀ represent the position vector and…

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

A: