Find the value of alpha so that A vector =2icap-jcap+kcap,B vector=ICAP+2jcap-3kcap and C vector=3icap+alphajcap+5kcap are coplanar.
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Explanation:
Three vectors, a, b, c are coplanar if [abc]=0
or
∣
∣
∣
∣
∣
∣
∣
∣
2
1
3
−1
2
λ
1
−3
5
∣
∣
∣
∣
∣
∣
∣
∣
=0
or 2(10+3λ)+1(5+9)+1(λ−6)=0 ( expanding along first row.)
or 7λ+28=0∴λ=−4
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