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Mathematics Question on Vector Algebra

Find the sum of the vectors a⃗=i^−2j^+k^,b⃗=−2i^+4j^+5k^\vec{a}=\hat{i}-2\hat{j}+\hat{k},\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k} and c⃗=i^−6j^−7k^.\vec{c}=\hat{i}-6\hat{j}-7\hat{k}.

Answer

The correct answer is:−4j^−k^-4\hat{j}-\hat{k}
The given vectors are a⃗=i^−2j^+k^,b⃗=−2i^+4j^+5k^\vec{a}=\hat{i}-2\hat{j}+\hat{k},\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k} and c⃗=i^−6j^−7k^.\vec{c}=\hat{i}-6\hat{j}-7\hat{k}.
∴a⃗+b⃗+c⃗=(1−2+1)i^+(−2+4−6)j^+(1+5−7)k^∴\vec{a}+\vec{b}+\vec{c}=(1-2+1)\hat{i}+(-2+4-6)\hat{j}+(1+5-7)\hat{k}
=0.i^−4j^−1.k^=0.\hat{i}-4\hat{j}-1.\hat{k}
=−4j^−k^=-4\hat{j}-\hat{k}