Suppose we have the triangle with vertices P(1,6, 1), Q(-3,7,–3), and R(5, 1, 1). Answer the following questions. 1. Find a non-zero vector orthogonal to the plane through the points P, Q, and R. Answer: 2. Find the area of the triangle APQR. Area:

Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: Find the area of the parallelogram that has the vectors as adjacent sides. AB= 6i + 6j - 6k, AD = 6i…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are find the cross product

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: 21. Given F₁ = 3î - 2ĵ+ 4k and F₂ = 5j + k, find: a. Dot product, F₁ F₂ = b. Dot product, F₂ · F₁ =…

A: As per our guidelines we are suppose to solve only first three subparts if the multiple parts are…

Q: Given the vectors v and u, answer a. through d. below. v = 2i + 3j - 6k u= 5i + 12j a. Find the dot…

A: Given v=2i+3j-6ku=5i+12jWe know that i.i=j.j=k.k=1i.j=j.k=k.i=0

Q: What is the area of the parallelogram generated by the vectors a = 8i +3j-ky b-i-j+10k? A. 101.58 B.…

A: We have to find the area of the parallelogram generated by the two vector

Q: - Using the parallelogram in Problem 44 as a base, cre- ate a parallelopiped with side P, P; where…

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Q: Consider the points P(-1, 1, 0), Q(2, -1,2), and R(1, 1, 3). Show your work for the compu- tations…

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Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: Ifv+w= and v = [1]. C W= , compute and draw the vectors v and w.

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Q: draw a set of x-,y-, z- and axes and plot the following position vectors (including rectangular…

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Q: Assume that the coordinates of the points P, Q, R, S, and O are as follows: P(-3, 2) Q(6, 4) R(4, 3)…

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