Learn Vectors with Examples, Equations, and Practice Problems

Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors $A = (2, 1, - 4), B = (- 3, 0, 1)$
Angle between the vectors A and B What is the angle $θ A B$ between A and B? Express your answer numerically to three significant figures in radians. $θ A B =$ radians

eozoischgc 2021-12-16

Find the unit vectors that are parallel to the tangent line to the curve $y = 2 \sin x$ at the point $(\frac{π}{6}, 1)$

Gregory Jones 2021-12-16

Derivative of cross-product of two vectors $\frac{d}{d t} [\vec{u (t)} \times \vec{v (t)}]$ , is it possible to find the cross-product of the two vectors first before differentiating?

Carole Yarbrough 2021-12-16

How do you find the unit vector in the direction of the given vector of $v = < 5, - 12 >$ ?

Marla Payton 2021-12-15

Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors $A (2, 1, 4), B = (- 3, 0, 1), C = (- 1, - 1, 2)$
Dot product of a vector and a scalar? Which of the following can be computed? Which of the following can be computed?
a) $\overset{―}{A} \cdot \overset{―}{B} \cdot \overset{―}{C}$
b) $\overset{―}{A} \cdot (B \cdot \overset{―}{C})$
c) $\overset{―}{A} \cdot (\overset{―}{B} + \overset{―}{C})$
d) $3 \overset{―}{A}$

Michael Maggard 2021-12-15

Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors $B = (- 3, 0, 1), C = (- 1, - 1, 2)$
Dot product of two vectors multiplied by constants Calculate $2 \overset{―}{B} \cdot 3 \overset{―}{C}$ . Express your answer numerically. $2 \overset{―}{B} \cdot 3 \overset{―}{C} =$

zgribestika 2021-12-15

Can vectors be inverted in this question?
Enquire if it is possible to solve the below for C.
$B^{- 1} (x - μ) = x c$
Here obviously B is an invertible matrix and both c and μ are column vectors.
Would the solution be $x^{- 1} B^{- 1} (x - μ) = c$ is it possible to invert vectors ?
How about if it was the other way
$B^{- 1} (x - μ) = c x$
Is there any other way to do this ?

stop2dance3l 2021-12-14

Projection of u onto v and v onto u
Given the vector $u = < - 2, 6, 4 >$ and a vector v such that the vector projection of u onto v is $< 2, 4, 4 >$ , and the vector projection of v onto u is $< - 8, 24, 16 >$ . What is the vector v?
Let $\vec{v} = < a, b, c >$
Projection of $\vec{v} o n \to \vec{u}$ is given by:
$p r o j_{u} v = \frac{\vec{u} . \vec{v}}{{| u |}^{2}} \vec{u} = \frac{\vec{u} . \vec{v}}{{(- 2)}^{2} + 6^{2} + 4^{2}} < - 2, 6, 4 >$
$< - 8, 24, 16 \geq \frac{\vec{u} . \vec{v}}{{(- 2)}^{2} + 6^{2} + 4^{2}} < - 2, 6, 4 >$
$\Rightarrow 4 < - 2, 6, 4 \geq \frac{\vec{u} . \vec{v}}{4 + 36 + 16} < - 2, 6, 4 >$
$\Rightarrow < - 2, 6, 4 \geq \frac{\vec{u} . \vec{v}}{224} < - 2, 6, 4 >$
On comparing $\frac{\vec{u} . \vec{v}}{224} = 1$
$\Rightarrow \vec{u} . \vec{v} = 224$
$p r o j_{v} u = \frac{\vec{u} . \vec{v}}{{| v |}^{2}} \vec{v} = \frac{224}{{| v |}^{2}} < a, b, c >$
$\Rightarrow < 2, 4, 4 \geq \frac{224}{{| v |}^{2}} < a, b, c >$
Dividing both sides by 2 we get:
$\Rightarrow < 1, 2, 2 \geq \frac{112}{{| v |}^{2}} < a, b, c >$

Sallie Banks 2021-12-08

What does this notation mean?
$| | \frac{\partial x}{\partial s} \times \frac{\partial x}{\partial t} | |$

puntgewelb5 2021-12-05

The curves $r_{1} (t) = ⟨ t, t^{2}, t^{3} ⟩ and r_{2} (t) = ⟨ \sin t, \sin 2 t, t ⟩$ intersect at the origin. Find their angle of intersection correct to the nearest degree.

grislingatb 2021-11-19

Tell the opposite to a cross product.
For example, $a \times b = c$ . How to find c, if you know only a and b?

grislingatb 2021-11-17

Solve the initial value problem for
$r$
as a vector function of t. Differential equation:
$\frac{d^{2} r}{{d t}^{2}} = - 32 k$
Initial conditions:
r(0)=100k and
$\frac{d r}{d t} ∣_{t = 0} = 8 i + 8 j$

gonjenjemeb 2021-11-17

Find a unit vector that has the same direction as the given vector. -3i + 7j

smismSitlougsyy 2021-11-16

Identify the surface with the given vector equation.
$r (s, t) = < s \sin 2 t, s^{2}, s \cos 2 t >$

luipieduq3 2021-11-14

Write the solution of the given homogeneous system in parametric vector form
$3 x_{1} + 3 x_{2} + 6 x_{3} = 0$
$- 9 x_{1} - 9 x_{2} - 18 x_{3} = 0$
$- 6 x_{2} - 6 x_{3} = 0$
where the solution set is $x = [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}]$

yapafw 2021-11-14

Find the angle $θ$ between the given vectors to the nearest tenth of a degree.
$U = - 5 i + 7 j, V = 8 i + 3 j$

sfair24bz 2021-11-13

Find an equation of the plane passing through the point perpendicular to the given vector or line. Point: (3, 2, 2) Perpendicular to: n = 2i + 3j - k

inlays85k5 2021-11-13

Find the curl and of the vector field.
$F (x, y, z) = (x + y z) i + (y + x z) j + (z + x y) k$

gainejavima 2021-11-13

Use the dot product to find an angle between $u = 5 i + 2 j$ and $v = 8 i - 3 j$ to the nearest tenth of a degree.

inlays85k5 2021-11-13

Find the vector v that has the same direction as u and the given magnitude. Magnitude ||v|| = 10 Direction u = ⟨-3. 4⟩

Vectors in the Precalculus course are usually more challenging since there are different vectors examples that are always mentioned. For example, if you are majoring in Engineering disciplines, you will have to use more than one approach to explain the most efficient ways. Take a look at vectors practice problems that have been presented below. It will help you learn and find the answers that will let you see the best equation and graphs. At the same time, when you are dealing with vectors equations, do not forget about unknown coefficients as you are looking for combinations and various solutions.

Precalculus

Vector Examples, Equations, and Practice Problems