Free solutions to high school vectors problems - PlainMath

Recent questions in Vectors

asked 2021-09-21

Find, correct to the nearest degree, the three angles of the triangle with the given vertices.

A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)

ANSWERED

asked 2021-09-17

Find the vector, not with determinants, but by using properties of cross products. \(\displaystyle{\left({i}\times{j}\right)}\times{k}\)

ANSWERED

asked 2021-09-15

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

ANSWERED

asked 2021-09-09

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

ANSWERED

asked 2021-09-03

Find a vector function that represents the curve of intersection of the two surfaces. The cylinder \(\displaystyle{x}^{{2}}+{y}^{{2}}={4}\) and the surface z=xy

ANSWERED

asked 2021-08-22

Find the volume of the parallelepiped determined by the vectors a, b, and c. \(a=<1, 2, 3>, b=<-1, 1, 2>, c=<2, 1, 4>\)

ANSWERED

asked 2021-08-22

Use the cross product to find a vector that is orthogonal to both u and v. u = (1, 1, -2), v = (2, -1, 2)

ANSWERED

asked 2021-08-20

Find the vector, not with determinants, but by using properties of cross products. \(\displaystyle{\left({i}+{j}\right)}\times{\left({i}-{j}\right)}\)

ANSWERED

asked 2021-08-20

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

ANSWERED

asked 2021-08-20

Find the scalar and vector projections of b onto a.
\(\displaystyle{a}={\left({4},{7},-{4}\right)},{b}={\left({3},-{1},{1}\right)}\)

ANSWERED

asked 2021-08-19

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

ANSWERED

asked 2021-08-19

Two vectors, a and b, are unit vectors with an angle of 60 degrees between them (when tail-to-tail).
If the vectors below are orthogonal, what is the value(s) of m?
u= a-3b
v=ma + b

ANSWERED

asked 2021-08-18

Determine whether the vectors u and v are parallel, orthogonal, or neither.
\(\displaystyle{u}=⟨−{3},{4}⟩,{v}−⟨\frac{{20}}{{15}}⟩\)
\(\displaystyle{u}=⟨−{3},{4}⟩,{v}−⟨\frac{{20}}{{15}}⟩\)

ANSWERED

asked 2021-08-18

Find the scalar product of the two vectors A and B.
Find the angle between these two vectors.
\(\displaystyle{A}=−{2.00} ı+{6.00} ȷ {\quad\text{and}\quad} {B}={2.00} ı−{3.00} ȷ\)

ANSWERED

asked 2021-08-17

Find an equation for the plane containing the two (parallel) lines
\(\displaystyle{v}_{{1}}={\left({0},{1},-{2}\right)}+{t}{\left({2},{3},-{1}\right)}\)
and \(\displaystyle{v}_{{2}}={\left({2},-{1},{0}\right)}+{t}{\left({2},{3},-{1}\right)}.\)

ANSWERED

asked 2021-08-17

Find an equation for the plane that
(a) is perpendicular to \(\displaystyle{v}={\left({1},{1},{1}\right)}\) and passes through (1,0,0).
(b) is perpendicular to \(\displaystyle{v}={\left({1},{2},{3}\right)}\) and passes through (1,1,1)
(c) is perpendicular to the line \(\displaystyle{l}{\left({t}\right)}={\left({5},{0},{2}\right)}{t}+{\left({3},-{1},{1}\right)}\) and passes through (5,-1,0)
(d) is perpendicular to the line \(\displaystyle{l}{\left({t}\right)}={\left(-{1},-{2},{3}\right)}{t}+{\left({0},{7},{1}\right)}\) and passes through (2,4,-1).

ANSWERED

asked 2021-08-17

The three straight lines y = x, 7y = 2x, and 4x + y = 60 form a triangle. Find the coordinates of its vertices.

ANSWERED

asked 2021-08-16

Determine whether the given vectors are orthogonal, parallel, or neither. u = ⟨-3, 9, 6⟩, v = ⟨4, -12, -8⟩

ANSWERED

asked 2021-08-15

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

ANSWERED

asked 2021-08-15

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

1
2
3
4

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