Question

Determine whether the given vectors are perpendicular. u = 2i − 3j, v = −12i − 8j

Answer 1

The vectors u and v are perpendicular because their dot product is zero, confirming that they are orthogonal vectors.

Step-by-step explanation:

To determine whether the given vectors u = 2i − 3j and v = −12i − 8j are perpendicular, we can use the dot product of the vectors. Two vectors are perpendicular or orthogonal if their dot product is zero.

The dot product of vectors u and v is calculated as follows:

1. First, multiply the corresponding components of the vectors: (2)(−12) + (−3)(−8).
2. Then, sum the products: −24 + 24.
3. The sum of the products is 0, which means the vectors are indeed perpendicular.

Therefore, vectors u and v are perpendicular to each other as their dot product equals zero, confirming they are orthogonal vectors.