Study guide and
13 practice problems
on:
Vector scalar multiplication
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Study Guide
$c \mathbf{x}$ is the vector obtained by multiplying the length of $\bfx$ by $c$.
(6 problems)
$c \langle x_1, x_2, x_3 \rangle = \langle c x_1, c x_2, c x_3 \rangle.$
(2 problems)
For any scalar $c$ and vector $\mathbf{x}$, $|c \mathbf{x} | = |c|\ |\mathbf{x} |$.
(4 problems)
Related topics
Vectors
(55 problems)
Multivariable calculus
(147 problems)
Practice problems
Find the vector of length 2 in the direction of $\langle 1,-1 \rangle$.
Solution
Estimate what positive multiples of the following vectors add up to zero.
Solution
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
Let $\mathbf{z}$ be the point one third of the way from $\mathbf{x}$ to $\mathbf{y}$. Using vector arithmetic, express $\mathbf{z}$ in terms of $\mathbf{x}$ and $\mathbf{y}$.
Solution
For a scalar $c$ and a vector $\bfx$, show that $\left |c\bfx \right| = \left |c\right | \ \left |\bfx \right|.$
Solution
Find a unit vector in the direction of $\langle 1, 1 \rangle$.
Solution
Suppose that two opposite sides of a quadrilateral are parallel and have equal length. Show that the quadrilateral is a parallelogram.
Solution
Show that the line connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.
Solution
more problems