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If |veca|=4and-3lelamdale2, then the ran...

If `|veca|=4and-3lelamdale2`, then the range of `|lamdaveca|` is

A

[8,0]

B

[-12,8]

C

[0,12]

D

[8,12]

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `|veca|=4and-3lelamdale2`
`:.|lamdaveca|=|lamda||veca|=lamda|4|`
`implies|lamdaveca|=|-3|4=12,atlamda=-3`
`|lamdaveca|=|0|4=0,atlamda=0`
and `|lamdaveca|=|2|4=8,atlamda=2`
So, the range of `|lamdaveca|" is " [0,12]`
Alternate Method
Since, `-3lelamdale2`
`0le|lamda|le3`
`implies0le4|lamda|le12`
`|lamdaveca|in[0,12]`
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