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Find the dot product of two vectors vec(...

Find the dot product of two vectors `vec(A)=3hat(i)+2hat(j)-4hat(k)` and `vec(B)=2hat(i)-3hat(j)-6hat(k)`.

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To find the dot product of the vectors \(\vec{A} = 3\hat{i} + 2\hat{j} - 4\hat{k}\) and \(\vec{B} = 2\hat{i} - 3\hat{j} - 6\hat{k}\), we will follow these steps: ### Step 1: Identify the components of the vectors The components of vector \(\vec{A}\) are: - \(A_x = 3\) (coefficient of \(\hat{i}\)) - \(A_y = 2\) (coefficient of \(\hat{j}\)) - \(A_z = -4\) (coefficient of \(\hat{k}\)) ...
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