Let ܽ\(\vec{a}=4 \hat{\imath}-2 \hat{\jmath}+6 \hat{k} \text { and } \vec{b}=7 \hat{\imath}+\hat{\jmath}-12 \hat{k} . \text { If } \vec{a} \times \vec{b}=α \hat{\imath}+β \hat{\jmath}+γ \hat{k}\), then the value of α + β + γ equals _______.
Enter numerical value using the virtual keypad. Round off where necessary.