Find a · b.
a = 8i + j,    b = i − 9j + k


To find the dot product \( a \cdot b \) between two vectors \( a \) and \( b \), you can use the following formula:

\[
a \cdot b = (a_1 \cdot b_1) + (a_2 \cdot b_2) + (a_3 \cdot b_3)
\]

Given:
\[
a = 8i + j + 0k
\]
\[
b = i - 9j + k
\]

The components are:
- \( a = (8, 1, 0) \)
- \( b = (1, -9, 1) \)

Now, apply the dot product formula:

\[
a \cdot b = (8 \cdot 1) + (1 \cdot -9) + (0 \cdot 1)
\]
\[
a \cdot b = 8 - 9 + 0
\]
\[
a \cdot b = -1
\]

Thus, \( a \cdot b = -1 \).

Would you like more details on this? Here are some related questions to expand on the concept:

1. What is the geometric interpretation of the dot product?
2. How can you find the angle between two vectors using the dot product?
3. What is the cross product of two vectors, and how does it differ from the dot product?
4. Can the dot product of two vectors ever be greater than the product of their magnitudes?
5. What happens to the dot product if two vectors are perpendicular?

**Tip:** The dot product can help determine whether two vectors are perpendicular, as it will be zero if they are.

Find a · b.
a = 8i + j,
b = i − 9j + k

Discover how to calculate the dot product of the vectors a = 8i + j and b = i − 9j + k using the dot product formula. This vector algebra problem is perfect for students in Grades 9-12 and explores key concepts like vector components and the dot product theorem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation