Consider the points A(3,-1, 3), B(4, -3,0), C(-2, -2,0), and D(6, 3,-5). (a) Find the volume of the parallelepiped that has the vectors AB, AC, and AD as adjacent edges. NOTE: Enter the exact answer. Volume = (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the exact answer. Distance: -

Q: nd the distance from the point to the plane.   (3,3,8)​, 7y+3

A: Given, the equation of plane is                                       7y+3z=0and  point (3, 3, 8)

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Find the volume of a parallelepiped spanned by 2i - 5j - 7k, i-k and 9i – 3k.

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Q: Find the equation of the plane parallel to the line r = 2i + t(−4i + 3j + 8k) and containing the…

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Q: Consider the points A(3,-3, 2), B(6, -5,0), C(-1, –4,0), and D(6,3,-4). (a) Find the volume of the…

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Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: Consider the points A(3, –3, 5), B(5, –5, 2), C'(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of…

A: AB→=(5, -5, 2)-(3, -3, 5)AB→=(2, -2, -3)AC→=(-1, -4, 2)-(3, -3, 5)AC→=(-4, -1, -3)AD→=(4, 1, -8)-(3,…

Q: Consider the points A(1, –1, 2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). | (a) Find the volume of…

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Q: Q6. Find the volume of parallelopiped formed by the vectors , and .

A: To find the volume of the parallelepiped formed by given vectors.

Q: Give v that is perpendicular to a plane containing (1,2,3), (3, 4, 1) and (-1, -2, -3). Check if…

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Q: Consider the points A(1, -1, 2), B(2, –3,0), C(-1,-2,0), and D(2,1, –1). (a) Find the volume of the…

A: Here, the given vectors are: A(1,-1,2), B(2,-3,0), C(-1,-2,0) & D(2,1,-1) (a) Here,…

Q: Let A = (-2,-2) and B= (2,-2) betwo points and AB subtends an ang in the plane in such a way that…

A: Since AB=4 and area of AAPB is 8,we have                 1 2×4×h=8 or h=4where h is the height of…