Find parametric equations for lines passing through point Pand parallel to vector n: (а) Р(3, — 1, 2): n — (2, 1, 3) (b) Р(— 2, 3, — 3): в — (6, — 6, — 2)

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: Find parametric equations for the line whose vector equation is given (a) (x, y) = (3, –5) + t(1,…

A: A)x, y =3, -5 + t 1, -2x, y =3, -5 + t, -2tx, y =3+t, -5-2t Parametric equations of the line:x= 3 +…

Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

A:

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

A:

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: Topic = vector

Q: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

A:

Q: Find a vector equation for the line segment from (2, -4, 6) to (5, 5, 5). (Use the parameter t.)…

A: a→=2i-4j+6kb→=5i+5j+5kn→=b→-a→=3i+9j-k

Q: | Find a vector equation for the line through the point (–9, –9, 3) parallel to the line 19 + 4t, y…

A:

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given that : P = ( 1, 0 ) and d = -13 .

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: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

A:

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

A:

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: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

A:

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: Find the equation of a line in vector form that is parallel to 3x−2y+z= 4, passes through the point…

A:

Q: If a line is parallel to the vector 4i + 10j + 7k and passes through the point P = (7,7,4), then the…

A: Solution

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

A:

Q: Find a vector equation for the line segment from (2, -4, 5) to (6, 4, 4). (Use the parameter t.)…

A: Explanation of the solution is given below...

Q: Find a vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

Q: Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). 1+t ,te…

A: The vector equation of the line passing through the points A(x1,y1,z1) and B(x2,y2,z2)  is given by;…

Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

A:

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

A:

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A:

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

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

A:

Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

A:

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

A:

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

A:

Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

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

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

Q: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…

Q: snip1

A: The given point is, P=1,2,-1 which is parallel to the vector d=5-13. The objective is to find the…

Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

A:

Q: Give a vector parametric equation for the line through the point (-2, –2) that is perpendicular to…

A:

Q: Find the vector equation of the line between the points (3, -1, 2) & (1, 4, -1), then graph the…

A:

Q: Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the xy-plane through the point…

A:

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

A:

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: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…