There are exactly two unit vectors perpendicular to the vector $\vec { i } + 2 \vec { j } + \vec { k }$ .

Question

Quizplus · Accepted Answer

There is only one unit vector perpendicular to any given non-zero vector in three-dimensional space, which can be found using the cross product with another non-zero vector not parallel to the original. However, this process yields a specific direction, and normalizing it gives a single unit vector. The confusion might arise from the fact that the vector and its negative would both be perpendicular, but normalization to unit length doesn't change this fundamental directionality.

There Are Exactly Two Unit Vectors Perpendicular to the Vector i⃗+2j⃗+k⃗\vec { i } + 2 \vec { j } + \vec { k }i+2j​+k

There Are Exactly Two Unit Vectors Perpendicular to the Vector $\vec { i } + 2 \vec { j } + \vec { k }$