Study guide and
4 practice problems
on:
Length of a scalar vector multiplication
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For any scalar $c$ and vector $\mathbf{x}$, $|c \mathbf{x} | = |c|\ |\mathbf{x} |$, where $|c|$ is the absolute value of $c$.
Related topics
Length of a vector
(32 problems)
Vectors
(55 problems)
Multivariable calculus
(147 problems)
Vector scalar multiplication
(13 problems)
Practice problems
Let $c$ be a nonzero scalar. Does $c \ \mathbf{x}$ have the same direction as $\mathbf{x}$?
Solution
For what value(s) of $c$ is $c (\textbf{i} + \textbf{j} + \textbf{k})$ a unit vector?
Solution
If $\text{dir } \mathbf{x} = \text{dir } \mathbf{y}$ show that $|\mathbf{x} + \mathbf{y}| = |\mathbf{x}| + | \mathbf{y} |$.
Solution
Does the vector projection of $\bfx$ along $\bfv$ depend on the length of $\bfv$? That is, if $\bfv$ is scaled by a scalar $c$, does the projection change?
Solution