The vector `vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk` are sides of a triangle ABC. The length of the median through A is (A) `sqrt(18)` (B) `sqrt(72)` (C) `sqrt(33)` (D) `sqrt(288)`

Options

A. `sqrt(14)`
B. `sqrt(18)`
C. `sqrt(29)`
D. `5`

Answer

B

Explanation

`vec(AB) + vec(AC) = 2vec(AD)`
`therefore vec(AD) = (1)/(2) {(-3hati+ 4hatk) + (5hati- 2hatj + 4hatk)}`
`" "= hati-hatj+ 4hatk`
Length of AD = `sqrt(1+1+ 16) = sqrt(18)`