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Prove that the value of the following d...

Prove that the value of the following determinant is zero: `|{:(a_(1),,la_(1)+mb_(1),,b_(1)),(a_(2),,la_(2)+mb_(2),,b_(2)),( a_(3),,la_(3)+mb_(3),,b_(3)):}|`

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(a) Operating `C_(2)-lC_(1)-mC_(3).` we get the value of the determinant is 0
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Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)=0 a_(2)x+b_(2)y+c_(2)=0

Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(1)hati + b_(2)hatj + b_(3)hatk and vecc=c_(1)hati +c_(2)hatj +c_(3)hatk be three non-zero vectors such that vecc is a unit vector perpendicular to both vectors, veca and vecb . If the angle between veca and vecb is pi//6 "then" |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|^(2) is equal to

Represent the following linear equations in matrix form: a_(1)x+b_(1)y+c_(1)z+d_(1)=0 , a_(2)x+b_(2)y+c_(2)z+d_(2)=0 and a_(3)x+b_(3)y_+c_(3)z+d_(3)=0

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