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Let veca=4veci+3vecj and vecb=3veci+4vec...

Let `veca=4veci+3vecj` and `vecb=3veci+4vecj`. a.Find the magnitudes of
a.`veca`,
b. `vecb`,
c.` veca+vecb `
d. `veca-vecb.`

Text Solution

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The correct Answer is:
(a) 5 (b) 5 (c) `7sqrt(2)` (d)2
`veca=4veci+vecj, vecb=3veci+4vecj`
(a). `|vecalpha|=sqrt(9+16)=5`
(b).`|vecb|=|3veci+4vech|=sqrt(9+16)=5`
(c).`|veca-vecb|=|7veci+7vecj|=sqrt(49+49)`
`sqrt(98)=7sqrt(2)`
(d). `veca-vecb=(4veci+3vecj)-(3veci+4vecj)`=`veci-vecj, rarr |veca-vecb|=sqrt((1)^2+(-1)^2)=2`
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