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If veca and vecb are non-collinear vecto...

If `veca and vecb` are non-collinear vectors and `vecA= (p+4q)veca+ (2p+q+1)vecb and vecB= (-2p+q+2)veca+ (2p-3q-1)vecb`, and if `3vecA= 2vecB`, then determine `p and q`.

Text Solution

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Putting the values of `vecA and vecB`, and then equating the coefficients of `veca and vecb` on both sides, we get
`" "3(p+4q) = 2(-2p+q+2)`
`" "3(2p+q+1)= 2(2p-3q-1)`
`" "7p+10q=4 and 2p+9q=-5`
Solving, we get `p=2 and q=-1`
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