question_answer

Vectors :\[\vec{A}=\text{3\hat{i}}+\text{5\hat{j}}-\text{2\hat{k}}\] and\[\vec{B}=-\text{3\hat{j}}+\text{6\hat{k}}\]. Find the vector\[\vec{C}\], such that\[2\vec{A}+7\,\vec{B}+4\vec{C}=0\].

Answer:

As\[2\vec{A}+7\,\vec{B}+4\vec{C}=0\];                so\[\vec{C}=-\frac{1}{4}[2\vec{A}+7\,\vec{B}]-\frac{1}{4}[\text{2}(\text{3\hat{i}}+\text{5\hat{j}}-\text{2\hat{k}})+\text{7}(-\text{ 3\hat{j}}+\text{6\hat{k}})]\] \[=-[\text{6\hat{i}}-\text{11\hat{j}}+\text{38\hat{k}}]=\text{1}.\text{5\hat{i}}+\text{2}.\text{75\hat{j}}-\text{9}.\text{5\hat{k}}\]