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

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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

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