Given a=i^−3j^;b=−2i^+5j^;c=3i^−j^a = \hat{i} - 3\hat{j}; b = -2\hat{i} + 5\hat{j}; c = 3\hat{i} - \hat{j}a=i^−3j^;b=−2i^+5j^;c=3i^−j^
a−b+c=(1−(−2)+3)i^+(−3−5+(−1))j^=6i^−9j^a - b + c = (1 - (-2) + 3)\hat{i} + (-3 - 5 + (-1))\hat{j} = 6\hat{i} - 9\hat{j}a−b+c=(1−(−2)+3)i^+(−3−5+(−1))j^=6i^−9j^
∣a−b+c∣=62+(−9)2=36+81=117\left| a - b + c \right| = \sqrt{6^{2} + (-9)^{2}} = \sqrt{36 + 81} = \sqrt{117}∣a−b+c∣=62+(−9)2=36+81=117
=9×13=313= \sqrt{9 \times 13} = 3\sqrt{13}=9×13=313
