Gandalf the Grey started in the forest of Mirkwood at a point with coordinates (3,-1) and arrived in the iron hills at the point with coordinates (5,2). If he began walking in the direction of the vector v = 4i + 1j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn?

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A: To find the vector equation of the line team C must follow if they wish to meet the team A at Right…

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A: Here we use vector application.

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A:

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A: To find the vector equation of a linewhose symmetric equations are   x-12=y+33=z-1-4.

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Q: 9. Illustrate how you would find the unit vector having the same direction as vector (p.q.r).

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A: The solution to the the given question is explained below.

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A: Given : 1)V=-5,32)V=2i+6j   To Find : 1) 12v2)  -v3)  4v

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A:

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A: Topic = vector

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A: topic = vectors

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Q: If the magnitude and direction of vector ? are 2√5and 153.3°, what are the components of vector ??

A: Simplification of vector

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A: The given points are;  P1=(5,-1,-5) and P2=(2,7,-13).

Q: Find a vector in the same direction as (-5, 2, –3) with magnitude 6.

A: In this question , firstly we can find the unit vector of the given vector and after that we can…

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Q: Express the vector -8i-4j-8k as a product of its length and direction.

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Q: . Find the direction cosines of the vector joining the two points (4, 2, 2) and (7, 6, 14).

A: Given that: Two points are (4, 2, 2) and (7, 6, 14)

Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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A: topic - vectors

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Q: How do we know if two nonzero vectors are perpendicular?

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Q: If a = 3i-j-4k, b - 2i + 4j-3k and c i+2j-k. Find unit vector parallel to 3 a -2 b +4 c. Q.1

A: Comment:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…