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: 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: +d. A e. f. the angle between vectors PQ and PR the area of the triangle with vertices at P, Q, and…

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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: Find the lengths of triangle PQR. Is it a right triangle? Is the triangle equilateral, scalene, or…

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Q: Q9: Showthat triangle ABC is right at A where A(1,0,1), B(2,1,0), c (1, 2, 3).

A: Question No. (9):To show that triangle ABC is right at A where . Note: Since the student has posted…

Q: 1. Three vectors are given by: å = 2î – 3ĵ + 5k, b = -2î + 7j – k and č = lî + 2j – 4k. axb Find a,…

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Q: Q2: Find the angle between the vectors à and b where a = i+ 2j – k and b = -i+j-2k.

A: The angle between two vectors A→ and B→ is calculated as, cosθ=A→.B→AB The given vectors are,…

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: . Find the angle between the vectors å = 4i – 35 + k and b = 21 – k. (First find an exact expression…

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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: Given the triangle ABC below with A(4, 3); B(7, -1) and C(2, -2). Answer the following questions:…

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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: Given the vectors v =i+ 3j – 2k and w = 3i – 4j + k. Find the area of the parallelogram with sides…

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Q: The three vertices of a triangle are at A (7,-1,3), B (-3,3,-4) and C(-3,1, 5). Find: (use Dot…

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Q: i+ 2j+ k and w = 2i - j+ 4k. Find the area of the parallelogram with sides given as v and w. !!

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Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…