What is the distance from the origin of the point, the vector from the origin to which is represented by the vector 3i + 4j + 5k

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A vector has both a magnitude as well as a direction. You cannot have a vector represent a single point. A vector is always from a point A to another point B.

Taking 3i + 4j + 5k to be the vector from the origin O to the point A, you would like to know the distance of the point A from the origin. This is given by the magnitude of the vector.

The magnitude of a vector A = ax*i + bx*j + cx*k is sqrt(a^2 + b^2 + c^2)

|3i + 4j + 5k| = sqrt(3^2 + 4^2 + 5^2) = sqrt(9 + 16 + 25) = sqrt 50.

The distance of the given point from the origin where 3i + 4j + 5k represents the vector from the origin to the point is equal to sqrt 50.

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