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Find the vector of length 3 unit which...

Find the vector of length 3 unit which is perpendicular to ` hat i+ hat j+ hat k` and lies in the plane of ` hat i+ hat j+ hat k and 2 hat i-3 hat j` .

Text Solution

Verified by Experts

Given vectors are
`veca=hati+hatj+hatk`
`vecb=hati+hatj+hatk`
`vecc=2hati-3hatj`
vector perpendicular to vectors `vecb and vecc is vecb xx vecc`.
vector perpendicular to `veca and vecb xx vecc is veca xx(vecb xx vecc)` which lies in the pllane of `vecb and vecc`. therefore
`vecaxx(vecbxxvecc)=[(hati+hatj+hatk)xx{(hati+hatj+hatk)xx(2hati-3hatj)}]`
`(hati+hatj+hatk)-3(2hati-3hatj)`
`= - 7 hati + 8 hatj-hatk`
`(vecaxx(vecbxxvecc))/(|vecaxx(vecbxxvecc)|) = (-7hati+8hatj-hatk)/sqrt114`
Required vector = `3(vecaxx(vecbxxvecc))/(|vecaxx(vecb xxvecc)|)=3(-7hati+8hatj-hatk)/sqrt114`
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