If the volume of a parallelepiped with coterm | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The volume of a parallelepiped with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is given by the scalar triple product $|\vec{a} \cdot (\vec{b} \

Vedclass · Accepted Answer

$-13$

Vedclass · Answer

(B) The volume of a parallelepiped with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is given by the scalar triple product $|\vec{a} \cdot (\vec{b} 	imes \vec{c})|$,which is equal to the absolute value of the determinant of the matrix formed by these vectors.Given edges: $\vec{a} = 4 \hat{i} + 5 \hat{j} + \hat{k}$,$\vec{b} = 0 \hat{i} - 1 \hat{j} + 1 \hat{k}$,$\vec{c} = 3 \hat{i} + 9 \hat{j} + p \hat{k}$.Volume $= |	ext{det}(\vec{a}, \vec{b}, \vec{c})| = 34$.$\Rightarrow \left|\begin{array}{rrr} 4 & 5 & 1 \ 0 & -1 & 1 \ 3 & 9 & p \end{array}ight| = \pm 34$.Expanding the determinant along the first row:$4(-p - 9) - 5(0 - 3) + 1(0 - (-3)) = \pm 34$.$-4p - 36 + 15 + 3 = \pm 34$.$-4p - 18 = \pm 34$.Case $1$: $-4p - 18 = 34 \Rightarrow -4p = 52 \Rightarrow p = -13$.Case $2$: $-4p - 18 = -34 \Rightarrow -4p = -16 \Rightarrow p = 4$.Since $-13$ is one of the options,the correct value is $-13$.

List-$I$	List-$II$
$1$. Nitrogen molecules	$(A)$ Continuous spectrum
$2$. Incandescent solids	$(B)$ Absorption spectrum
$3$. Fraunhoffer lines	$(C)$ Band spectrum
$4$. Electric arc between iron rods	$(D)$ Emission spectrum

If the volume of a parallelepiped with coterminous edges $4 \hat{i} + 5 \hat{j} + \hat{k}$,$-\hat{j} + \hat{k}$,and $3 \hat{i} + 9 \hat{j} + p \hat{k}$ is $34$ cubic units,then $p$ is equal to:

Similar Questions

The number of atoms in $100 \ g$ of an $fcc$ crystal with density $d = 10 \ g/cm^3$ and cell edge length $a = 100 \ pm$ is:

$A$ galvanometer having a coil resistance of $60\,\Omega$ shows full-scale deflection when a current of $1.0\,A$ passes through it. It can be converted into an ammeter to read currents up to $5.0\,A$ by:

The harmonic mean of $\frac{a}{1 - ab}$ and $\frac{a}{1 + ab}$ is

Match the appropriate pairs from List-$I$ and List-$II$ :
List-$I$ List-$II$
$1$. Nitrogen molecules $(A)$ Continuous spectrum
$2$. Incandescent solids $(B)$ Absorption spectrum
$3$. Fraunhoffer lines $(C)$ Band spectrum
$4$. Electric arc between iron rods $(D)$ Emission spectrum

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module