Question

Write an expression for the vector difference a⃗ −b⃗ using unit vectors.

Answer 1

To express the vector difference a⃗ - b⃗ with unit vectors, you add the negative of b⃗ to a⃗.

Step-by-step explanation:

The vector difference between a→ and b→ can be expressed using unit vectors by subtracting vector b→ from vector a→. This is equivalent to adding the negative of vector b→ to vector a→.

So, the expression for the vector difference a→ - b→ using unit vectors is a→ + (-b→).

Answer 2

A vector A with components a, b, c can be written as (a, b, c) or in terms of unit vectors as ai + bj + ck. The letters i, j, k are the standard symbols for the unit vectors in the x, y and z directions.

So if A = (3, 4, 5), you can also write A = 3i + 4j + 5k
If B = (1, 1, 1), you can write B = i + j + k
And then A - B is the vector whose components are the differences in each component: A - B = (3 - 1)i + (4 - 1)j + (5 - 1)k = 2i + 3j + 4k

So you need to know what the components of A and B are to answer this.