Solution: For two vectors to be orthogonal, their dot product must be zero. Compute the dot product:

Thu, 07 May 2026 10:21:31 +0000

Understanding Orthogonal Vectors: The Essential Role of the Dot Product In linear algebra, one of the fundamental concepts is orthogonality between vectors. Two vectors are considered orthogonal if their dot product equals zero. This condition is not only elegant but also powerful, underpinning key ideas in geometry, physics, computer graphics, and machine learning. ### What Does It Mean for Vectors to Be Orthogonal? Orthogonality means that two vectors meet at a right angle (90°). While we often visualize vectors as arrows in space, mathematically, their dot product measures how much one vector extends in the direction of another. When the dot product is zero, it confirms there is no projection of one vector onto the other — hence, the angle between them is 90°.