Question

If a = 3i - 4j, b = 2i - 5j and c = λi + μj

where λ and μ are scalar quantities, find the λ and μ such that λc = 2a + 3b

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Answer 1

hi,

Explanation:

`\left\{\begin{array}{ccc}a&=&3*\vec{i}-4\vec{j}\\b&=&2*\vec{i}-5\vec{j}\\c&=&\lambda*\vec{i}+\mu*\vec{j}\\\end{array}\right.\\\\\\\lambda*c=2a+3b\\=2*(3*\vec{i}-4\vec{j})+3*(2*\vec{i}-5\vec{j})\\=12*\vec{i}-23\vec{j}\\=\lambda*(\lambda*\vec{i}+\mu*\vec{j})\\\\\\\left\{\begin{array}{ccc}\lambda^2&=&12\\\lambda*\mu&=&-23\end{array}\right.\\\\\\\left\{\begin{array}{ccc}\lambda&=&2√(3)\\\mu&=&(-23*√(3) )/(6) \\\end{array}\right.\\`