Given that a=3i-2j, b=3i+j and c=-6i+j, express pa-qb in terms of p,q,i and j. Hence, find the value of p and of q if pa-qb is equal to the unit vector along the straight line 4x+3y=12
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Since it has been a while: It is, as I said, integer arithmetic. pa= p(3i- 2j)= 3pi- 2pj. qb= q(3i+ j)= 3qi+ qj. pa- qb= 3pi- 2pj- (3qi+ qj)= (3p- 3q)i-(2p+ q)j.Given that a=3i-2j, b=3i+j and c=-6i+j, express pa-qb in terms of p,q,i and j. Hence, find the value of p and of q if pa-qb is equal to the unit vector along the straight line 4x+3y=12
A vector pointing along the straight line 4x+ 3y= 12 is 4i+ 3j which has length $\displaystyle \sqrt{4^2+ 3^2}= 5$ so a unit vector in that direction is (4/5)i+ (3/5)j
We have (3p- 3q)i- (2p+ q)j= (4/5)i+ (3/5)j so solve 3p- 3q= 4/5 and -2p- q= 3/5 for p and q.