An object flying in air with velocity \( (20 \hat{i}+25 \hat{j}-12 \hat{k}) \) suddenly breaks i....

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An object flying in air with velocity \( (20 \hat{i}+25 \hat{j}-12 \hat{k}) \) suddenly breaks in two pieces
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whose masses are in the ratio \( 1: 5 \). The smaller mass flies off with a velocity \( (100 \hat{i}+35 \hat{j}+8 \hat{k}) \). The velocity of the largest piece will be
(1) \( 4 \hat{i}+23 \hat{j}-16 \hat{k} \)
(2) \( -100 \hat{i}-35 \hat{j}-8 \hat{k} \)
(3) \( 20 \hat{i}+15 \hat{j}-80 \hat{k} \)
(4) \( -20 \hat{i}-15 \hat{j}-80 \hat{k} \)


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