1 A = Bì+45+6k and B = 4ì + 5î - gk Determine the dot produc between A and B and the angle between them.

Given the vectors \( A = B\mathbf{i} + 45 + 6k \) and \( B = 4\mathbf{i} + 5\mathbf{j} - g\mathbf{k} \), we are tasked with determining the **dot product** of \( A \) and \( B \), and the **angle** between them.

### Step 1: Express Vector A Clearly

From the problem, it seems like the vector \( A \) is defined as a combination of \( B \) and other terms. First, rewrite \( A \) explicitly.

Given:
\[
A = B\mathbf{i} + 45 + 6\mathbf{k}
\]
We interpret this as:
\[
A = B\mathbf{i} + 45\mathbf{j} + 6\mathbf{k}
\]

Now substitute \( B = 4\mathbf{i} + 5\mathbf{j} - g\mathbf{k} \).

Thus, \( A \) becomes:
\[
A = (4\mathbf{i} + 5\mathbf{j} - g\mathbf{k})\mathbf{i} + 45\mathbf{j} + 6\mathbf{k}
\]

It seems there may be a misunderstanding in the problem's statement, but if we proceed as described, we first clarify if this is what you intend.

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Let me know if you need further clarification on the vector expressions or have questions before continuing to the dot product and angle.

A = Bì + 45 + 6k and B = 4ì + 5î - gk. Determine the dot product between A and B and the angle between them.

Learn how to calculate the dot product and angle between vectors A = Bì + 45 + 6k and B = 4ì + 5î - gk using vector algebra. This problem covers key concepts like the dot product formula and the angle between vectors. Suitable for students in Grades 10-12.

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