Learn Vectors with Examples, Equations, and Practice Problems

Calculate the cross product of the following:
$(3 j - 2 k) \times (6 j + k)$

geduiwelh 2021-08-11

Determine whether the vectors $υ_{1} = (- 1, 2, - 3), υ_{2} = (3, 2, 1), υ_{3} = (5, 6, - 1)$ are linearly dependent or independent in $R^{3} .$

cistG 2021-06-20

v is a set of ordered pairs (a, b) of real numbers. Sum and scalar multiplication are defined by: $(a, b) + (c, d) = (a + c, b + d) k (a, b) = (k b, k a)$ (attention in this part) show that V is not linear space.

Alyce Wilkinson 2021-06-12

Find the vector, not with determinants, but by using properties of cross products. $k \times (i - 2 j)$

Mylo O'Moore 2021-06-10

Find an equation for the plane containing the two (parallel) lines
$v_{1} = (0, 1, - 2) + t (2, 3, - 1)$
and $v_{2} = (2, - 1, 0) + t (2, 3, - 1) .$

Cabiolab 2021-06-09

Find the vector, not with determinants, but by using properties of cross products. $(i + j) \times (i - j)$

Khadija Wells 2021-06-08

Vector A = 5i +1j and vector B = 2i -6j +2k
What is the cross product of $A \times B$ ,
find the x component?
Find the y component?
Find the z component?

usagirl007A 2021-06-07

Find two unit vectors that make an angle of $60^{\circ}$ with v=<3,4>

Yasmin 2021-06-07

Find the curve’s unit tangent vector. Also, find the length of the indicated portion of the curve.
$r (t) = (2 \cos t) i + (2 \sin t) j + \sqrt{5} t k, 0 \leq t \leq π$

tinfoQ 2021-06-06

Let vectors $A^{'} = (2, 1, - 4)$
$B^{'} = (- 3, 0, 1)$
and $C^{'} = (- 1, - 1, 2)$
Calculate the following:
$2 (B^{'} \cdot 3 C^{'}) = ?$

UkusakazaL 2021-06-04

Vectors $V_{1}$ and $V_{2}$ are different vectors with lengths $V_{1}$ and $V_{2}$ respectively. Find the following:
a) $V_{1} \cdot V_{1}$ Express you answer in terms of $V_{1}$
b) $V_{1} \cdot V_{2}$ , when they are perpendicular
c) $V_{1} \cdot V_{2}$ , when they are parallel

Lipossig 2021-06-04

Find the vectors' orthogonality, parallelism, or lack thereof. u = ⟨-3, 9, 6⟩, v = ⟨4, -12, -8⟩

Amari Flowers 2021-06-03

Let vectors $\bar{A} = (2, 1, - 4), \bar{B} = (- 3, 0, 1), and \bar{C} = (- 1, - 1, 2)$
Calculate the following:
A) $\bar{A} \cdot \bar{B}$ ?
E)Which of the following can be computed?
$\bar{A} \cdot \bar{B} \cdot \bar{C}$
$\bar{A} (\bar{B} \cdot \bar{C})$
$\bar{A} (\bar{B} + \bar{C})$
$3 \bar{A}$
F)Express your answer in terms of $v_{1}$
G) If $v_{1} and v_{2}$ are perpendicular?
H) If $v_{1} and v_{2}$ are parallel?

CMIIh 2021-06-02

Find the angle between the given vectors . Round to the nearest tenth of a degree.
1) u= -3i +6j ,v=5i + 2j
2) u= i -j , v=2i +3j
Use the dot product to determiine wheter the vectors are parallel, orthogonal , or neither .
1) v = 2i +j, w = i-2j
2) v = 4i-j , w=8i-2j
3) v= 3i +3j , w=3i -2j
Find proj w v
1) v = 2i +3j . w = 8i- 6j
2) v= 2i -3j . w =-3i +j

smileycellist2 2021-06-01

Find the vector, not with determinants, but by using properties of cross products. $(i \times j) \times k$

sodni3 2021-05-29

Find the vector and parametric equations for the line segment connecting P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

chillywilly12a 2021-05-29

Which of the following expressions are meaningful? Which are meaningless? Explain.
a) $(a \cdot b) \cdot c$
$(a \cdot b) \cdot c$ has ? because it is the dot product of ?.
b) $(a \cdot b) c$
$(a \cdot b) c$ has ? because it is a scalar multiple of ?.
c) $| a | (b \cdot c)$
$| a | (b \cdot c)$ has ? because it is the product of ?.
d) $a \cdot (b + c)$
$a \cdot (b + c)$ has ? because it is the dot product of ?.
e) $a \cdot b + c$
$a \cdot b + c$ has ? because it is the sum of ?.
f) $| a | \cdot (b + c)$
$| a | \cdot (b + c)$ has ? because it is the dot product of ?.

Emeli Hagan 2021-05-28

Find a unit vector that is orthogonal to both i+j and i+k.

sagnuhh 2021-05-28

Find the maximum rate of change off at the given point and the direction in which it occurs.
$f (x, y) = 4 y \sqrt{x}, (4, 1)$

Zoe Oneal 2021-05-27

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.
$L 1 : \frac{x}{1} = \frac{y - 1}{- 1} = \frac{z - 2}{3}$
$L 2 : \frac{x - 2}{2} = \frac{y - 3}{- 2} = \frac{z}{7}$

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