Two perpendicular vectors 𝐔 and 𝐕 lie in the x-y plane. The vector 𝐔=6 𝐢-8 𝐣 and |𝐕|=20. What ar

step 1 Today we're going to calculate the cross product between u equals 0 minus 2 0 and v, which equal

Two perpendicular vectors 𝐔 and 𝐕 lie in the x-y plane. The...

Two perpendicular vectors $\mathbf{U}$ and $\mathbf{V}$ lie in the $x-y$ plane. The vector $\mathbf{U}=6 \mathbf{i}-8 \mathbf{j}$ and $|\mathbf{V}|=20$. What are the components of $\mathbf{V}$ ?

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Key Concepts

Dot Product

The dot product is an operation on two vectors that results in a scalar. It is computed as the sum of the products of the corresponding components of each vector. Importantly, the dot product is used to determine the angle between vectors; when the dot product is zero, the vectors are perpendicular.

Perpendicular Vectors

Two vectors are perpendicular if their dot product equals zero. This property is crucial in many areas of vector analysis and geometry since it gives a method to confirm orthogonality between vectors in any dimensional space.

Magnitude of a Vector

The magnitude (or length) of a vector is a measure of its size and is computed as the square root of the sum of the squares of its components. In problems involving vectors, knowing the magnitude is essential for scaling, normalization, and comparison purposes.

Vector Components

Vectors in a plane can be represented by their components along the coordinate axes. Understanding how to break a vector into its x and y components allows for easy manipulation and analysis, such as combining vectors or using conditions like perpendicularity to solve for unknown components.

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