 Recent questions in Vectors
Vectors

### 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)

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

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

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

Vectors
ANSWERED ### 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

Vectors
ANSWERED ### Find the volume of the parallelepiped determined by the vectors a, b, and c. $$a=<1, 2, 3>, b=<-1, 1, 2>, c=<2, 1, 4>$$

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

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

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

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

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

Vectors
ANSWERED ### 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

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

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

Vectors
ANSWERED ### 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 $$\displaystyle{v}_{{2}}={\left({2},-{1},{0}\right)}+{t}{\left({2},{3},-{1}\right)}.$$

Vectors
ANSWERED ### 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).

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

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

Vectors
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