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Two vectors vecAandvecB of magnitude 5 u...

Two vectors `vecAandvecB` of magnitude 5 units and 7 units make an angle `60^(@)` with each other. Find the magnitude of the difference vector `vecA-vecB` and its direction with respect to the vector `vecA`.

Text Solution

Verified by Experts

Using the equation,
`|vecA-vecB|=sqrt(5^(2)+7^(2)-2xx5xx7cos60^(@))=sqrt(25+49-35)=sqrt39` units
The angle that `vecA-vecB` makes with the vector `vecA` is given by
`tanalpha_(2)=(7sin60^(@))/(5-7cos60^(@))=(7sqrt3)/(10-7)=(7)/(sqrt3)=4.041`
`alpha_(2)=tan^(-1)(4.041)=76^(@)`
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