Given u=11i-5j and v=-7i+10j, what is u•v

To find the dot product \( u \cdot v \) of the two vectors \( u = 11\mathbf{i} - 5\mathbf{j} \) and \( v = -7\mathbf{i} + 10\mathbf{j} \), we use the formula:

\[
u \cdot v = (u_1 \cdot v_1) + (u_2 \cdot v_2)
\]

where \( u_1 \) and \( u_2 \) are the components of vector \( u \), and \( v_1 \) and \( v_2 \) are the components of vector \( v \).

Substituting the given values:

\[
u \cdot v = (11)(-7) + (-5)(10)
\]

Now, calculate each term:

\[
u \cdot v = -77 - 50 = -127
\]

So, the dot product \( u \cdot v \) is \(-127\).

Would you like details on how the dot product works or have any questions?

Here are 5 related questions to consider:
1. How do you find the magnitude of a vector?
2. What is the significance of a dot product being negative?
3. How do you compute the angle between two vectors using the dot product?
4. What is the cross product, and how does it differ from the dot product?
5. How can you determine if two vectors are orthogonal using the dot product?

**Tip:** The dot product of two perpendicular vectors is always zero, which can help determine if they are orthogonal.

Learn how to calculate the dot product of vectors u = 11i - 5j and v = -7i + 10j using the dot product formula. Understand the significance of dot products in vector mathematics. Suitable for high school students and anyone interested in vector algebra.

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