Question

what is a unit vector in the direction of the vector A=4i+3j.

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Answer 1

Answer:

HOPE..IT..HELPS..

Answer 2

Concept:

A unit vector is one with a magnitude of 1. It is mathematically expressed as, a^ = a/ |a|

Given:

Vector, A = 4i + 3j

Find:

We need to determine the unit vector in the director of a vector.

Solution:

A quantity with both magnitude and direction is referred to as a vector.

A unit vector is one with a magnitude of 1.

It also goes by the name Direction Vector.

Mathematically, it is expressed as-

A^ = A/ |A|

|a| can be calculated by the square root of the sum of the squares of the vector components.

|A| = √(4²+3²) = √(16 + 9)

|A| = √25 = 5

Therefore, equation of unit vector becomes, A^ = A/ |A|

A^ = 4i + 3j / 5

A^ = 4/5 i + 3/5 j

Thus, the unit vector in the direction of  A=4i+3j is 4/5 i + 3/5 j.

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