Question

If `veca = hati - hatj + hatk, vecb = 2hati + λhatj + hatk, vecc = hati - hatj + 4hatk` and `veca.(vecb xx vecc)` = 10, then λ is equal to ______.

Options

• 6

• 7

• 9

• 10

Answer 1

If `veca = hati - hatj + hatk, vecb = 2hati + λhatj + hatk, vecc = hati - hatj + 4hatk` and `veca.(vecb xx vecc)` = 10, then λ is equal to 6.

Explanation:

Given, `veca = hati + hatj + hatk`, `vecb = 2hati + λhatj + hatk` and `vecc = hati - hatj + 4hatk` is 

As, `veca.(vecb xx vecc)` = 10

`\implies [(1, 1, 1),(2, λ, 1),(1, -1, 4)]` = 10

`\implies` 1(4 λ + 1) – 1(8 – 1) + 1(– 2 – λ) = 10

`\implies` 4 λ + 1 – 7 – 2 – λ = 10

`\implies` 3 λ = 18

`\implies` λ = 6