If three vectors vec{a} = 12hat{i} + 4hat{j} | vedclass

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

Question

(D) The volume of a parallelepiped defined by vectors $\vec{a}, \vec{b},$ and $\vec{c}$ is given by the scalar triple product $|[\vec{a} \, \vec{b} \,

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The volume of a parallelepiped defined by vectors $\vec{a}, \vec{b},$ and $\vec{c}$ is given by the scalar triple product $|[\vec{a} \, \vec{b} \, \vec{c}]|$.$V = |\vec{a} \cdot (\vec{b} 	imes \vec{c})| = \left| \det \begin{bmatrix} 12 & 4 & 3 \ 8 & -12 & -9 \ 33 & -4 & -24 \end{bmatrix} ight|$Expanding the determinant along the first row:$V = |12((-12)(-24) - (-9)(-4)) - 4((8)(-24) - (-9)(33)) + 3((8)(-4) - (-12)(33))|$$V = |12(288 - 36) - 4(-192 + 297) + 3(-32 + 396)|$$V = |12(252) - 4(105) + 3(364)|$$V = |3024 - 420 + 1092|$$V = |3696| = 3696 	ext{ cubic units.}$Since $3696$ is not among the options,the correct choice is $(d)$.

If three vectors $\vec{a} = 12\hat{i} + 4\hat{j} + 3\hat{k}$,$\vec{b} = 8\hat{i} - 12\hat{j} - 9\hat{k}$,and $\vec{c} = 33\hat{i} - 4\hat{j} - 24\hat{k}$ represent the coterminous edges of a parallelepiped,then its volume is:

Similar Questions

If $a = i - j + k$,$b = i + 2j - k$ and $c = 3i + pj + 5k$ are coplanar,then the value of $p$ is:

If $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$,$\vec{b} = 2\hat{i} + 3\hat{j} - \hat{k}$,and $\vec{c} = \lambda\hat{i} + \hat{j} + (2\lambda - 1)\hat{k}$ are coplanar vectors,then $\lambda$ is equal to:

If the vectors $2i - 3j + 4k$, $i + 2j - k$ and $xi - j + 2k$ are coplanar, then $x = $

If the volume of a tetrahedron,whose vertices are $A(1, 2, 3)$,$B(-3, -1, 1)$,$C(2, 1, 3)$,and $D(-1, 2, x)$ is $\frac{11}{6}$ cubic units,then the value of $x$ is:

If $a, b, c$ are distinct positive numbers and vectors $a \hat{\imath} + a \hat{\jmath} + c \hat{k}$,$\hat{\imath} + \hat{k}$,and $c \hat{\imath} + c \hat{\jmath} + b \hat{k}$ lie in a plane,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module