Let vec{a} = 2hat{i} - 3hat{j} + hat{k}, vec{ | vedclass

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

Question

(C) To check if the vectors are linearly independent or dependent, we calculate the scalar triple product $[\vec{a} \vec{b} \vec{c}]$, which is the de

Vedclass · Accepted Answer

Linearly independent

Vedclass · Answer

(C) To check if the vectors are linearly independent or dependent, we calculate the scalar triple product $[\vec{a} \vec{b} \vec{c}]$, which is the determinant of the matrix formed by the components of the vectors.$[\vec{a} \vec{b} \vec{c}] = \begin{vmatrix} 2 & -3 & 1 \ 3 & 2 & 2 \ 4 & -3 & 1 \end{vmatrix}$$= 2(2(1) - 2(-3)) - (-3)(3(1) - 2(4)) + 1(3(-3) - 2(4))$$= 2(2 + 6) + 3(3 - 8) + 1(-9 - 8)$$= 2(8) + 3(-5) + 1(-17)$$= 16 - 15 - 17 = -16$Since the scalar triple product is not zero, the vectors are linearly independent.

Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$, $\vec{b} = 3\hat{i} + 2\hat{j} + 2\hat{k}$, and $\vec{c} = 4\hat{i} - 3\hat{j} + \hat{k}$. The vectors $\vec{a}, \vec{b}, \text{ and } \vec{c}$ are:

Similar Questions

If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}$ and $\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}$ are coplanar,then $\lambda$ is the root of the equation

If $\overline{a}, \overline{b}$ and $\overline{c}$ are three non-coplanar vectors,then $(\overline{a}+\overline{b}+\overline{c}) \cdot[(\overline{a}+\overline{b}) \times(\overline{a}+\overline{c})]$ equals

If $a, b,$ and $c$ are unit coplanar vectors,then the scalar triple product $[a, b, c]$ is equal to:

The scalar $\overline{a} \cdot [(\overline{b} + \overline{c}) \times (\overline{a} + \overline{b} + \overline{c})]$ equals

If the vectors $2i - j + k$,$i + 2j - 3k$,and $3i + \lambda j + 5k$ are coplanar,then $\lambda = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module