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Consider three vectors vecA =hati+hatj-...

Consider three vectors `vecA =hati+hatj-2hatk,vecB=hati-hatj+hatk and vecC =2hati-3hatj+4hatk` . A vector `vecX` of the form `alpha vecA+betavecB(alpha and beta ` are numbers ) is perpendicular to `vecC` . The ratio of `alpha and beta` is

A

`1:1`

B

`2:1`

C

`-1:1`

D

`3:1`

Text Solution

Verified by Experts

The correct Answer is:
A
`(alpha vecA+betavecB)*vecC=0`
or, `2(alpha+beta)-3(alpha-beta)+4(beta-2alpha)=0`
or, `-9alpha+9beta=0 or, alpha:beta =1:1`
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