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Question
Let \[\vec{A} = 5 \vec{i} - 4 \vec{j} \text { and } \vec{B} = - 7 \cdot 5 \vec{i} + 6 \vec{j}\]. Do we have \[\vec{B} = k \vec{A}\] ? Can we say \[\frac{\vec{B}}{\vec{A}}\] = k ?
Solution
If \[\vec{A} = 5 \vec{i} - 4 \vec{j}\text { and } \vec{B} = - 7 \cdot 5 \vec{i} + 6 \vec{j}\],then we have \[\vec{B} = k \vec{A}\] by putting the value of scalar k as \[- 1 . 5\] .
However, we cannot say that \[\frac{\vec{B}}{\vec{A}}\] = k, because a vector cannot be divided by other vectors, as vector division is not possible.
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