Maths · Vectors and scalars, the addition of vectors
If and are non-collinear vectors and \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{
If \( \vec{a} \) and \( \vec{b} \) are non-collinear vectors and \( \boldsymbol{A}=(\boldsymbol{p}+\mathbf{4} \boldsymbol{q}) \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{1}) \boldsymbol{b} \) \( \boldsymbol{B}=(-\mathbf{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{2}) \boldsymbol{a}+(\mathbf{2} \boldsymbol{p}-\boldsymbol{3} \boldsymbol{q}-\mathbf{1}) \boldsymbol{b} \) then determine \( p \) and \( q, \) so that \( 3 A= \) \( 2 B \)
- A. \( p=1 \) and \( q=-0.3 \)
- B. \( p=-1 \) and \( q=1.1 \)
- C. \( p=2 \) and \( q=-1 \)
- D. \( p=-2 \) and \( q=1.8 \)
Step-by-step solution
Since a and b are non-collinear, equate coefficients of a and b after scaling: 3(p+4q)=2(-2p+q+2) gives 7p+10q=4, and 3(2p+q+1)=2(2p-3q-1) gives 2p+9q=-5. Solving yields p=2, q=-1.
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