Find a vector that is orthogonal to the plane containing the points. (Orthogonal means perpendicular) P= (3,0,1), Q = (4, –2, 1) and R= (5,3, –1).

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 plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5),…

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Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: Find a direction vector for the line through (4, 5, 3) and (2, – 3, – 1).

A: to find the direction vector

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: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R =…

A: The answer is given below:

Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: 19

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Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

Q: Let A = (1, –1, 2) and B = (4, –2, 3). Solve for proj,B. %3D

A: As per the guidelines for the multiple questions I had solved the first question.

Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…

Q: Find the vector expression for the line that is the intersection of the planes 3x−3y−2z=−2 and…

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Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

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