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Find the vector equation of line passing...

Find the vector equation of line passing through point (1,2,-4) and perpendicular to two lines `(x-8)/3 = (y+19)/-16 = (z-10)/7 and (x-15)/3 = (y-25)/8 =(z-5)/-5`

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`L_3_|_L_1,L_3_|_L_1`
`P_3_|_P_1,P_3_|_P_2`
`P_3=vecP_1*vecP_2`
`=hati(24)-hatj36+72hatk`
`vecP_3=24hati+36hatj+72hatk`
`vecP_3=12(2hati+3hatj+6hatk)`
`A(1,2,-4)`
`vecr-vecA=lambdavecP_3`
...
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