hexaedru8p

2022-10-09

If a and c are unit vectors at an angle $\pi /3$ with each other and $(a\times (b\times c)).(a\times c)=5$, then what is the value of [a b c]? I just know the basic meaning of what are vector and scalar triple product. How do I do this question?

Salma Baird

Beginner2022-10-10Added 8 answers

We want to compute $a\cdot b\times c=-b\cdot a\times c$. We'll use $a\times (b\times c)=(a\cdot c)b-(a\cdot b)c$ so

$5=(a\times (b\times c))\cdot (a\times c)=(a\cdot c)(b\cdot a\times c).$

Hence

$[abc]=\frac{-5}{a\cdot c}=\frac{-5}{\mathrm{cos}\frac{\pi}{3}}=-10.$

$5=(a\times (b\times c))\cdot (a\times c)=(a\cdot c)(b\cdot a\times c).$

Hence

$[abc]=\frac{-5}{a\cdot c}=\frac{-5}{\mathrm{cos}\frac{\pi}{3}}=-10.$

Shawn Peck

Beginner2022-10-11Added 2 answers

Use $a\times (b\times c)=(a\cdot c)b-(a\cdot b)c$. Then

$(a\times (b\times c))\cdot (a\times c)=(a\cdot c)b\cdot (a\times c)-(a\cdot b)c\cdot (a\times c)=-(a\cdot b)[a,b,c]$

etc.

$(a\times (b\times c))\cdot (a\times c)=(a\cdot c)b\cdot (a\times c)-(a\cdot b)c\cdot (a\times c)=-(a\cdot b)[a,b,c]$

etc.

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix

$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$ 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)Whether f is a function from Z to R if

?

a) $f\left(n\right)=\pm n$.

b) $f\left(n\right)=\sqrt{{n}^{2}+1}$.

c) $f\left(n\right)=\frac{1}{{n}^{2}-4}$.How to write the expression ${6}^{\frac{3}{2}}$ in radical form?

How to evaluate $\mathrm{sin}\left(\frac{-5\pi}{4}\right)$?

What is the derivative of ${\mathrm{cot}}^{2}x$ ?

How to verify the identity: $\frac{\mathrm{cos}\left(x\right)-\mathrm{cos}\left(y\right)}{\mathrm{sin}\left(x\right)+\mathrm{sin}\left(y\right)}+\frac{\mathrm{sin}\left(x\right)-\mathrm{sin}\left(y\right)}{\mathrm{cos}\left(x\right)+\mathrm{cos}\left(y\right)}=0$?

Find $\mathrm{tan}\left(22.{5}^{\circ}\right)$ using the half-angle formula.

How to find the exact values of $\mathrm{cos}22.5\xb0$ using the half-angle formula?

How to express the complex number in trigonometric form: 5-5i?

The solution set of $\mathrm{tan}\theta =3\mathrm{cot}\theta $ is

How to find the angle between the vector and $x-$axis?

Find the probability of getting 5 Mondays in the month of february in a leap year.

How to find the inflection points for the given function $f\left(x\right)={x}^{3}-3{x}^{2}+6x$?

How do I find the value of sec(3pi/4)?