If bar{a}=hat{imath}+hat{jmath}+hat{k}, bar{b | vedclass

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

Question

(C) Given the equation $l \bar{a} + m \bar{b} + n \bar{c} = \overline{0}$.Substituting the vectors: $l(\hat{\imath} + \hat{\jmath} + \hat{k}) + m(2\ha

Vedclass · Accepted Answer

$10, -1, -4$

Vedclass · Answer

(C) Given the equation $l \bar{a} + m \bar{b} + n \bar{c} = \overline{0}$.Substituting the vectors: $l(\hat{\imath} + \hat{\jmath} + \hat{k}) + m(2\hat{\imath} - 2\hat{\jmath} + 2\hat{k}) + n(2\hat{\imath} + 3\hat{\jmath} + 2\hat{k}) = 0\hat{\imath} + 0\hat{\jmath} + 0\hat{k}$.Equating the components to zero:$l + 2m + 2n = 0$ $(i)$$l - 2m + 3n = 0$ (ii)$l + 2m + 2n = 0$ (iii)From $(i)$ and (iii),we see they are identical. Subtracting (ii) from $(i)$:$(l + 2m + 2n) - (l - 2m + 3n) = 0$$4m - n = 0 \implies n = 4m$.Substitute $n = 4m$ into $(i)$:$l + 2m + 2(4m) = 0 \implies l + 10m = 0 \implies l = -10m$.Let $m = -1$,then $l = 10$ and $n = -4$.Thus,the values are $(10, -1, -4)$.

If $\bar{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \bar{b}=2 \hat{\imath}-2 \hat{\jmath}+2 \hat{k}, \bar{c}=2 \hat{\imath}+3 \hat{\jmath}+2 \hat{k}$ are three vectors such that $l \bar{a}+m \bar{b}+n \bar{c}=\overline{0}$,then the values of $l, m, n$ are respectively

Similar Questions

If $C$ is the midpoint of $AB$ and $P$ is any point outside $AB$,then

Let $G$ be the centroid of a triangle $ABC$ and $O$ be any other point in that plane,then $\overline{OA}+\overline{OB}+\overline{OC}+\overline{OG}=$

If $ABCDEF$ is a regular hexagon with $\vec{AB} = \vec{a}$ and $\vec{BC} = \vec{b}$,then $\vec{CE}$ equals to

If $a = \hat{i} + 4 \hat{j}$, $b = 2 \hat{i} - 2 \hat{j}$, and $c = 5 \hat{i} + 9 \hat{j}$, then $c$ is equal to:

The perimeter of the triangle whose vertices have the position vectors $\hat{i}+\hat{j}+\hat{k}$,$5\hat{i}+3\hat{j}-3\hat{k}$,and $2\hat{i}+5\hat{j}+9\hat{k}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module