Question #9f838

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Answer 1 · 2016-09-30T20:45:40

Refer to the Explanation.

The Unit Vector in the direction of $- - \to A B$ $vec(AB)$ can definitely be

written as $\frac{1}{10} - - \to A B .$ $1/10vec(AB).$

This is justified because of an Operation known as

The Multiplication of a Vector by a Scalar.

For Example, multiplication of $\to x = 2 i + 3 j - 4 k$ $vecx=2i+3j-4k$ by a scalar $- \frac{1}{2}$ $-1/2$ ,

denoted as $- \frac{1}{2} (\to x), or, - \frac{1}{2} (2 i + 3 j - 4 k)$ $-1/2(vecx), or, -1/2(2i+3j-4k)$ , is another $\to y$ $vecy$

given by, $\to y = - \frac{1}{2} \to x$ $vecy=-1/2vecx$

$= (- \frac{1}{2} \cdot 2) i + (- \frac{1}{2} \cdot 3) j + (- \frac{1}{2} \cdot - 4) k$ $=(-1/2*2)i+(-1/2*3)j+(-1/2*-4)k$

$= - i - \frac{3}{2} j + 2 k .$ $=-i-3/2j+2k.$