If r=3i+2j-5k a=2i-j+k b=i+3j-2k c=-2i+j-3k such that r=la+mb+nc then
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Answer:
A.P
Step-by-step explanation:
(3,2,−5)=λ(2,−1,1)+μ(1,3,−2)+γ(−2,1,−3)
3=2λ+μ−2γ
2=−λ+3μ+γ
−5=λ−2μ−3γ
⎣
⎢
⎢
⎡
2
−1
1
1
3
2
−2
1
−3
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
λ
μ
ν
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
3
2
−5
⎦
⎥
⎥
⎤
R
2
→R
2
+R
3
⎣
⎢
⎢
⎡
2
0
1
1
1
−2
−2
−2
−3
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
λ
μ
ν
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
3
−3
−5
⎦
⎥
⎥
⎤
R
1
→R
1
−R
2
⎣
⎢
⎢
⎡
2
0
1
0
1
−2
0
−2
−3
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
λ
μ
ν
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
6
−3
−5
⎦
⎥
⎥
⎤
λ=3γ=2μ=1
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