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Multivariable Calculus

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Moderate

Projection Identities

MVCALC-XRIEJ5

Let ${\bf u}$ and ${\bf v}$ be two vectors that are of the same length, but are not constant multiples of each other.

Which of the following five statements is NOT ​true?

A

$||{\bf proj_v \ u}|| =||{\bf proj_u \ v}||$

B

The vector component of ${\bf u}$ that is orthogonal to ${\bf v}$ is of the same length as the vector component of ${\bf v}$ that is orthogonal to ${\bf u}$.

C

The projection of ${\bf u}$ onto ${\bf v}$ is equal to the projection of ${\bf u}$ onto $3{\bf v}$.

D

The projection of ${\bf u}$ onto ${\bf v}$ is equal to the projection of $3{\bf u}$ onto ${\bf v}$.

E

The vector component of ${\bf u}$ that is orthogonal to $2{\bf v}$ is of the same length as the vector component of ${\bf v}$ that is orthogonal to $5{\bf u}$.