Scelta multipla
If vector and vector calculate using and notation.
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14. Vectors
Unit Vectors and i & j Notation
Scelta multipla
Find the unit vector in the direction of .
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First, understand that a unit vector is a vector with a magnitude of 1 that points in the same direction as the original vector. To find the unit vector, we need to divide the original vector by its magnitude.
Calculate the magnitude of the vector \( \mathbf{v} = 12\mathbf{i} - 35\mathbf{j} \). The magnitude \( ||\mathbf{v}|| \) is given by \( \sqrt{12^2 + (-35)^2} \).
Simplify the expression for the magnitude: \( ||\mathbf{v}|| = \sqrt{144 + 1225} = \sqrt{1369} \).
The magnitude \( ||\mathbf{v}|| \) is 37, so the unit vector \( \mathbf{v}^ \) is obtained by dividing each component of \( \mathbf{v} \) by 37.
Thus, the unit vector \( \mathbf{v}^ \) is \( \mathbf{v}^ = \frac{12}{37}\mathbf{i} - \frac{35}{37}\mathbf{j} \).
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