Give the vector equation of the plane passing through P, Q, and R. P = (3, 3, 3), Q = (4, 0, 2), R = (0, 1, −1) 3 3 -3 0-0-4- = S 3 -1 X y Z 1 + t 000

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: X = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z…

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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: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: Find the vector equation for the line passing through the points P₁(-3, 6, 8) and P₂(−6, 0, 12). 0 0…

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

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

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Q: Which of the following equations define the plane passing through the points (3,0, 0), (0, –7,0),…

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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: Find the equation of the plane passing through three points A (-1, 2, 1), B (1,0, -2) , C(1, –1,1)

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

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Q: Find the equation of the plane through the points P (1,-1, 1) Q = (3,–1,3); R= (2,1,1).

A: We will find out the required equation of plane.