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Find the constant a so that the followin...

Find the constant a so that the following vectors are coplaner `2i-j+k, i+2j-3k, 3i+aj+5k`

A

` - 4 `

B

` - 2 `

C

`-1 `

D

` - 8 `

Text Solution

Verified by Experts

The correct Answer is:
D
Let ` a = 2i-j - k`,
` b = i+ 2 j - 3 k `
and `c=3i + lamda j + 5k `
If these vectors are coplanar, then ` [a bc] ` = 0
` rArr |{:(2,,-1,,-1),(1,,2,,-3),(3,,lamda,,5):}|= 0 `
` rArr 2 (10 + 3lamda ) + ( 5 + 9 ) - ( lamda - 6 ) = 0 `
` rArr 20 + 6 lamda + 14 - lamda + 6 = 0 `
` rArr 5 lamda + 40 = 0 `
` rArr lamda = -8 `
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