(a) Let the vertices of a triangle ABC have the following position vectors relative to some origin O: OA = 2i + 3j − k, OB = i + j + k, OC = j+2k i. Show these vectors and the triangle on a rough sketch.  ii. Evaluate all the internal angles of the triangle.  iii. Calculate the area of the triangle ABC .

Q: a = 3i - j - 4k, b = 2i +4j - 2k, c = -i +6k a. 4a - b b. b * (c - a) c. ||a * b|| d. the angle…

A: Solution : Given, a=3i-j-4k b=2i+4j-2k c=-i+6k a.) 4a-b=4(3i-j-4k)+2i+4j-2k =14i-18k b.)…

Q: Consider the vectors v = 6i + 3j and w = 2i - 5j. Blank 1: Find the dot product of v and w. Blank 2:…

A:

Q: 1. a. The points (3,-1,2) and (-1,3,-4) are the endpoints of a diameter of a sphere i. Determine the…

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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: Find ZJ. K 92° 45° M 88° 45° 135° 108°

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Q: A certain field is a rectangle with a perimeter of 922 feet. The length is 151 feet more than the…

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Q: Write, in your notebook, which vectors are represented in the Cartesian plane.

A: We know that, the position vector AB → between the points Ax1,y1 and Bx2,y2 is given by  AB→=x2-x1…

Q: 4. Find the angle between each pair of vectors. Round to two decimal places as necessary. a) (V3,…

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Q: Use the regular hexagon below to answer the following questions.

A: Given hexagon is regular

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u = 9i +3j +…

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Q: A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29° and 53° with…

A: We have to find tension in cable.

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.