Let overline{a}=hat{i}+2 hat{j}-hat{k} and ov | vedclass

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

Question

(D) Given,$\overline{b} 	imes \overline{c} = \overline{b} 	imes \overline{a}$.This implies $\overline{b} 	imes (\overline{c} - \overline{a}) = \ove

Vedclass · Accepted Answer

$-\frac{1}{2}$

Vedclass · Answer

(D) Given,$\overline{b} 	imes \overline{c} = \overline{b} 	imes \overline{a}$.This implies $\overline{b} 	imes (\overline{c} - \overline{a}) = \overline{0}$.Thus,$\overline{c} - \overline{a} = \lambda \overline{b}$ for some scalar $\lambda$,so $\overline{c} = \overline{a} + \lambda \overline{b}$.Given $\overline{c} \cdot \overline{a} = 0$,we have $(\overline{a} + \lambda \overline{b}) \cdot \overline{a} = 0$.This gives $|\overline{a}|^2 + \lambda (\overline{b} \cdot \overline{a}) = 0$.Calculating the values: $|\overline{a}|^2 = 1^2 + 2^2 + (-1)^2 = 6$ and $\overline{b} \cdot \overline{a} = (1)(1) + (1)(2) + (-1)(-1) = 1 + 2 + 1 = 4$.Substituting these: $6 + 4\lambda = 0 \Rightarrow \lambda = -\frac{6}{4} = -\frac{3}{2}$.Now,$\overline{c} = \overline{a} - \frac{3}{2} \overline{b}$.Then $\overline{c} \cdot \overline{b} = (\overline{a} - \frac{3}{2} \overline{b}) \cdot \overline{b} = \overline{a} \cdot \overline{b} - \frac{3}{2} |\overline{b}|^2$.We have $\overline{a} \cdot \overline{b} = 4$ and $|\overline{b}|^2 = 1^2 + 1^2 + (-1)^2 = 3$.Therefore,$\overline{c} \cdot \overline{b} = 4 - \frac{3}{2}(3) = 4 - \frac{9}{2} = -\frac{1}{2}$.

Let $\overline{a}=\hat{i}+2 \hat{j}-\hat{k}$ and $\overline{b}=\hat{i}+\hat{j}-\hat{k}$ be two vectors. If $\overline{c}$ is a vector such that $\overline{b} \times \overline{c}=\overline{b} \times \overline{a}$ and $\overline{c} \cdot \overline{a}=0$,then $\overline{c} \cdot \overline{b}$ is

Similar Questions

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

Let $\vec{a}=\hat{i}-2\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b} \times \vec{c}=\vec{b} \times \vec{a}$ and $\vec{c} \cdot \vec{a}=0,$ then $\vec{c} \cdot \vec{b}$ is equal to

The magnitude of the projection of the vector $2\hat{i} + 3\hat{j} + \hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2\hat{j} + 3\hat{k}$ is

If $\vec{a}+2 \vec{b}+3 \vec{c}=\vec{0}$ and $(\vec{a} \times \vec{b})+(\vec{b} \times \vec{c})+(\vec{c} \times \vec{a})=\lambda(\vec{b} \times \vec{c})$,then the value of $\lambda$ is

If $\overline{a} = \hat{i} + \hat{j} + \hat{k}$ and $\overline{b} = \hat{j} - \hat{k}$,then the vector $\overline{r}$ satisfying $\overline{a} \times \overline{r} = \overline{b}$ and $\overline{a} \cdot \overline{r} = 3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module