The scalars l and m such that la + mb = c, wh | vedclass

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

Question

(A) Given the equation $la + mb = c$.To find $l$,take the cross product of both sides with $b$:$(la + mb) 	imes b = c 	imes b$$l(a 	imes b) + m(b \

Vedclass · Accepted Answer

$l = \frac{(c 	imes b) \cdot (a 	imes b)}{|a 	imes b|^2}, \, m = \frac{(c 	imes a) \cdot (b 	imes a)}{|b 	imes a|^2}$

Vedclass · Answer

(A) Given the equation $la + mb = c$.To find $l$,take the cross product of both sides with $b$:$(la + mb) 	imes b = c 	imes b$$l(a 	imes b) + m(b 	imes b) = c 	imes b$Since $b 	imes b = 0$,we have $l(a 	imes b) = c 	imes b$.Taking the dot product of both sides with $(a 	imes b)$:$l(a 	imes b) \cdot (a 	imes b) = (c 	imes b) \cdot (a 	imes b)$$l|a 	imes b|^2 = (c 	imes b) \cdot (a 	imes b)$$l = \frac{(c 	imes b) \cdot (a 	imes b)}{|a 	imes b|^2}$.Similarly,to find $m$,take the cross product of the original equation with $a$:$(la + mb) 	imes a = c 	imes a$$l(a 	imes a) + m(b 	imes a) = c 	imes a$Since $a 	imes a = 0$,we have $m(b 	imes a) = c 	imes a$.Taking the dot product of both sides with $(b 	imes a)$:$m|b 	imes a|^2 = (c 	imes a) \cdot (b 	imes a)$$m = \frac{(c 	imes a) \cdot (b 	imes a)}{|b 	imes a|^2}$.

The scalars $l$ and $m$ such that $la + mb = c,$ where $a, b$ and $c$ are given vectors,are equal to

Similar Questions

If $\bar{a}$ and $\bar{b}$ are unit vectors such that $(\bar{a} + 2\bar{b})$ and $(5\bar{a} - 4\bar{b})$ are perpendicular to each other,then the angle between $\bar{a}$ and $\bar{b}$ is .....$^o$.

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{b}$ is perpendicular to $\vec{c}$. If $|\vec{a}|=2, |\vec{b}|=3, |\vec{c}|=5$ and $|\vec{a}+\vec{b}+\vec{c}|=4 \sqrt{3}$,then the angle between $\vec{a}$ and $\vec{c}$ is

Let $p$ and $q$ be the position vectors of $P$ and $Q$ respectively with respect to $O$ and $|p| = p, |q| = q.$ The points $R$ and $S$ divide $PQ$ internally and externally in the ratio $2 : 3$ respectively. If $\overrightarrow{OR}$ and $\overrightarrow{OS}$ are perpendicular,then:

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{c}|^{2}=8$. Then $|\vec{a}+2\vec{b}|^{2}+|\vec{a}+2\vec{c}|^{2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module