(a cdot i)i + (a cdot j)j + (a cdot k)k = | vedclass

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Question

(A) Let the vector $a$ be represented in terms of its components as $a = x i + y j + z k$.Then,the dot product of $a$ with the unit vectors $i, j, k$

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$a$

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(A) Let the vector $a$ be represented in terms of its components as $a = x i + y j + z k$.Then,the dot product of $a$ with the unit vectors $i, j, k$ are:$a \cdot i = (x i + y j + z k) \cdot i = x$$a \cdot j = (x i + y j + z k) \cdot j = y$$a \cdot k = (x i + y j + z k) \cdot k = z$Substituting these values into the given expression:$(a \cdot i)i + (a \cdot j)j + (a \cdot k)k = x i + y j + z k$Since $x i + y j + z k = a$,the expression simplifies to $a$.

$(a \cdot i)i + (a \cdot j)j + (a \cdot k)k = $

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