Let overline{a}=hat{j}-hat{k} and overline{c} | vedclass

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

Question

(A) Given $\overline{a} 	imes \overline{b} + \overline{c} = \overline{0}$,which implies $\overline{a} 	imes \overline{b} = -\overline{c}$.Taking the

Vedclass · Accepted Answer

$-\hat{i}+\hat{j}-2 \hat{k}$

Vedclass · Answer

(A) Given $\overline{a} 	imes \overline{b} + \overline{c} = \overline{0}$,which implies $\overline{a} 	imes \overline{b} = -\overline{c}$.Taking the cross product with $\overline{a}$ on both sides: $\overline{a} 	imes (\overline{a} 	imes \overline{b}) = -\overline{a} 	imes \overline{c}$.Using the vector triple product formula $\overline{a} 	imes (\overline{b} 	imes \overline{c}) = (\overline{a} \cdot \overline{c})\overline{b} - (\overline{a} \cdot \overline{b})\overline{c}$,we get $(\overline{a} \cdot \overline{b})\overline{a} - (\overline{a} \cdot \overline{a})\overline{b} = -\overline{a} 	imes \overline{c}$.Given $\overline{a} = \hat{j} - \hat{k}$,so $\overline{a} \cdot \overline{a} = 0^2 + 1^2 + (-1)^2 = 2$.Given $\overline{a} \cdot \overline{b} = 3$,so $3\overline{a} - 2\overline{b} = -\overline{a} 	imes \overline{c}$.Calculate $\overline{a} 	imes \overline{c} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 0 & 1 & -1 \ 1 & -1 & -1 \end{vmatrix} = \hat{i}(-1 - 1) - \hat{j}(0 - (-1)) + \hat{k}(0 - 1) = -2\hat{i} - \hat{j} - \hat{k}$.Thus,$2\overline{b} = 3\overline{a} + (\overline{a} 	imes \overline{c}) = 3(\hat{j} - \hat{k}) + (-2\hat{i} - \hat{j} - \hat{k}) = -2\hat{i} + 2\hat{j} - 4\hat{k}$.Therefore,$\overline{b} = -\hat{i} + \hat{j} - 2\hat{k}$.

Let $\overline{a}=\hat{j}-\hat{k}$ and $\overline{c}=\hat{i}-\hat{j}-\hat{k}$. Then the vector $\overline{b}$ satisfying $\overline{a} \times \overline{b}+\overline{c}=\overline{0}$ and $\overline{a} \cdot \overline{b}=3$,is

Similar Questions

Let $\vec{p}, \vec{q},$ and $\vec{r}$ be three non-coplanar unit vectors equally inclined to each other at an acute angle $\theta$. The value of $|\vec{p} \times (\vec{q} \times \vec{r})|$ is:

$\hat{a}, \hat{b}$,and $\hat{c}$ are three unit vectors such that $\hat{a} \times(\hat{b} \times \hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c})$. If $\hat{b}$ is not parallel to $\hat{c}$,then the angle between $\hat{a}$ and $\hat{b}$ is

If $\overline{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\overline{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$,then the value of $(\overline{a}-2 \overline{b}) \cdot \{(\overline{a} \times \overline{b}) \times (2 \overline{a}+\overline{b})\}$ is

If $\vec{x} \cdot \vec{y} = 0$ then,$(\vec{y} \times \vec{x}) \times \vec{x} = $ . . . . . . . where,$|\vec{x}| = 1$.

If $u = i \times (a \times i) + j \times (a \times j) + k \times (a \times k),$ then

Vedclass Test Series

Exam Paper Generator

Online Exam Module