Find the value of p, if the vectors ` hati - 2hatj + hatk `,
` 2hati - 5hatj + phatk and 5hati - 9hatj + 4hatk ` are coplanar .

Explanation

Let `bara = hati - 2hatj + hatk, barb = 2hati - 5hatj + phatk` and
` barc = 5hati - 9hatj + 4hatk " As " bara, barb, barc` are coplanar.
Therefore , ` bara , (barb xx barc) = 0 `
`therefore |{:(1,-2,1),(2,-5,p),(5,-9,4):}|= 0 `
` rArr 1 . (-20 + 9p) + 2 (8-5p) + 1.(-18 + 25) = 0 `
`rArr - 20 + 9p + 16 - 10p - 18 + 25 = 0 `
` rArr 3 - p = 0 `
` rArr p = 3 ` .