Let A = 2i – 3j and B = 2i + j, where i =< 1, 0 > and j =< 0, 1 > . Find each of the following. a. 2A + B b. || A|| c. The vector of magnitude one that is in the direction opposite to B.

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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.)…

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A: We have to find vector addition, subtraction, direction and modulus.

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Q: 3. Find a unit vector in the direction of v. V = 20i – 21j

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Q: Let a . Find a unit vector in the direction of a = 1 35 i + 5 √35 =j+ k 3 35 X Invalid notation.

A: Let's find unit vector in the direction of a.

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.