4. Find the equation of the plane containing the point (2, 7, −3) that is orthogonal to the line r(t) = 〈2−t, 4t, 5〉.

Q: Determine a vector equation for hte line through the point: (-2, 0, -8) perpendicular ot the plane:…

A:

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: The parametric vector v=(6-t)i+(9t+8)j represents a straight line. Find the equation of this line

A:

Q: A plane in R'is perpendicular to the vector (4, 2, – 9), and contains the point (- 9, 5, - 8). Find…

A: A plane in ℝ3 is perpendicular to the vector 4, 2, -9 and contains point -9, 5, -8To find the…

Q: Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector…

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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 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: 38. Find the component form and magnitude of the vector with beginning point at (-2, 1) and end…

A: It is given that, the vector begins from point (-2,-1) and terminates at point (1,3).

Q: Which of the following is a normal vector to the plane which is parallel to vectors (0,−3,1) and…

A:

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

A: