Question

Let `vecalpha = hati + 2hatj - hatk, vecbeta = 2hati - hatj + 3hatk, vecγ = 2hati + hatj + 6hatk`. If `vecalpha` and `vecbeta` are both perpendicular to a vector `vecδ` and `vecδ. vecγ` = 10, then the magnitude of `vecδ` is

विकल्प

• `sqrt(3)/2`

• `2sqrt(3)`

• `sqrt(3)`

• `1/sqrt(3)`

Answer 1

`2sqrt(3)`

Explanation:

Since `veca` and `vecbeta` are both perpendicular to a vector `vecS`

∴ `vecS = lambda (vecalpha xx vecbeta)`

= `lambda|(hati, hatj, hatk),(1, 2, -1),(2, -1, 3)| = 5lambdahati - 5hatj - 5lambdahatk`

Now, `vecS.vecγ` = 10

⇒ `(5lambdahati - 5lambdahatj - 5lambdahatk).(2hati + hatj + 6hatk)` = 10

⇒ `10lambda - 5lambda - 30lambda` = 10

⇒ `lambda = - 2/5`

∴ `|vecS| = sqrt(75lambda^2) = sqrt(75 xx 4/25) = 2sqrt(3)`