Final answer:
To find two unit vectors orthogonal to î and 9î + â, we perform a cross product yielding -à and the negation of this result, which is à. Both vectors are along the y-axis and orthogonal to the original vectors.
Step-by-step explanation:
To find two unit vectors that are orthogonal to both î and 9î + â, we can take their cross-product. According to the properties of cross products, the result will be orthogonal to both vectors. Since our given vectors already lie in the xz-plane, the resulting cross-product will be along the y-axis, due to the cyclic order of the unit vectors in three-dimensional space.
The original vectors can be written as (1, 0, 0) and (9, 0, 1) respectively. The cross-product of these vectors is obtained by computing the determinant of the following matrix:
| î à â |
| 1 0 0 |
| 9 0 1 |
Which results in:î(0*1 - 0*9) - à(1*1 - 0*9) + â(1*0 - 0*9) = 0î - 1à + 0â = -à
The resulting vector is -1à, which is already a unit vector and is orthogonal to both original vectors. The other orthogonal unit vector will be just the negation of this result, which is 1à, as negating a vector does not change its length but makes it point in the opposite direction.