If bar{a} and bar{b} are not perpendicular to | vedclass

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

Question

(B) Given $\bar{r} 	imes \bar{a} = \bar{b} 	imes \bar{a}$,we can write $\bar{r} 	imes \bar{a} - \bar{b} 	imes \bar{a} = 0$,which implies $(\bar{r}

Vedclass · Accepted Answer

$\bar{b} - \left(\frac{\bar{b} \cdot \bar{c}}{\bar{a} \cdot \bar{c}}\right) \bar{a}$

Vedclass · Answer

(B) Given $\bar{r} 	imes \bar{a} = \bar{b} 	imes \bar{a}$,we can write $\bar{r} 	imes \bar{a} - \bar{b} 	imes \bar{a} = 0$,which implies $(\bar{r} - \bar{b}) 	imes \bar{a} = 0$. This means that the vector $(\bar{r} - \bar{b})$ must be parallel to $\bar{a}$. Therefore,we can write $\bar{r} - \bar{b} = k\bar{a}$ for some scalar $k$,or $\bar{r} = \bar{b} + k\bar{a}$. We are also given $\bar{r} \cdot \bar{c} = 0$. Substituting the expression for $\bar{r}$ into this equation,we get $(\bar{b} + k\bar{a}) \cdot \bar{c} = 0$. Expanding this,we have $\bar{b} \cdot \bar{c} + k(\bar{a} \cdot \bar{c}) = 0$. Solving for $k$,we get $k = -\frac{\bar{b} \cdot \bar{c}}{\bar{a} \cdot \bar{c}}$. Substituting this value of $k$ back into the expression for $\bar{r}$,we get $\bar{r} = \bar{b} - \left(\frac{\bar{b} \cdot \bar{c}}{\bar{a} \cdot \bar{c}}ight) \bar{a}$.

If $\bar{a}$ and $\bar{b}$ are not perpendicular to each other,$\bar{r} \times \bar{a} = \bar{b} \times \bar{a}$ and $\bar{r} \cdot \bar{c} = 0$,then $\bar{r} =$

Similar Questions

If $a \cdot i = 4$,then $(a \times j) \cdot (2j - 3k) = $

Let $a, b, c$ be three vectors such that $a \neq 0$,$a \times b = 2a \times c$,$|a| = |c| = 1$,$|b| = 4$,and $|b \times c| = \sqrt{15}$. If $b - 2c = \lambda a$,then $\lambda$ equals:

Let $ABC$ be a triangle. Let $u = \overrightarrow{AB}$ and $v = \overrightarrow{AC}$. If $D$ is the midpoint of $BC$,then the length of the median of $\triangle ABD$ through the vertex $B$ is:

If $\bar{a} = \hat{i} + \hat{j}$ and $\bar{b} = 2\hat{i} - \hat{k}$,then the point of intersection of the lines $\bar{r} \times \bar{a} = \bar{b} \times \bar{a}$ and $\bar{r} \times \bar{b} = \bar{a} \times \bar{b}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module