Final answer:
To find two vectors in opposite directions that are orthogonal to vector u, we can use the concept of dot product. Let's assume vector u = [u1, u2], where u1 and u2 are the components of u. By setting v = [v1, v2] and solving the equation u · v = 0, we can find two orthogonal vectors [-u2, u1] and [u2, -u1].
Step-by-step explanation:
To find two vectors in opposite directions that are orthogonal to vector u, we can use the concept of dot product. The dot product of two vectors is zero if and only if the vectors are orthogonal. Therefore, we need to find two vectors that satisfy the equation u · v = 0, where · represents the dot product.
Let's assume vector u = [u1, u2], where u1 and u2 are the components of u. To find the orthogonal vectors, we can set v = [v1, v2] and solve the equation u · v = 0.
Expanding the dot product equation, we get u1 * v1 + u2 * v2 = 0. To satisfy this equation, we can choose v1 = -u2 and v2 = u1. Therefore, two vectors orthogonal to u are [-u2, u1] and [u2, -u1].