Let a, b and c be vectors with magnitudes 3, | vedclass

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(D) Given that $|a| = 3$,$|b| = 4$,and $|c| = 5$. Also,$a + b + c = 0$. Squaring both sides of the equation $a + b + c = 0$,we get: $|a + b + c|^2 = 0

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$-25$

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(D) Given that $|a| = 3$,$|b| = 4$,and $|c| = 5$. Also,$a + b + c = 0$. Squaring both sides of the equation $a + b + c = 0$,we get: $|a + b + c|^2 = 0^2$ $|a|^2 + |b|^2 + |c|^2 + 2(a \cdot b + b \cdot c + c \cdot a) = 0$ Substituting the given magnitudes: $3^2 + 4^2 + 5^2 + 2(a \cdot b + b \cdot c + c \cdot a) = 0$ $9 + 16 + 25 + 2(a \cdot b + b \cdot c + c \cdot a) = 0$ $50 + 2(a \cdot b + b \cdot c + c \cdot a) = 0$ $2(a \cdot b + b \cdot c + c \cdot a) = -50$ $a \cdot b + b \cdot c + c \cdot a = -25$.

Let $a, b$ and $c$ be vectors with magnitudes $3, 4$ and $5$ respectively and $a + b + c = 0$. Then the value of $a \cdot b + b \cdot c + c \cdot a$ is:

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