Question

If `veca + vecb = vecc ((λx)hati + yhatj + 4zhatk) + (yhati + xhatj + 3yhatk) = -zhati - 2zhatj - (λ + 1)xhatk` are sides of triangle as shown is figure then value of λ is ______.

(where x, y, z are not all zero)

Options

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Answer 1

If `veca + vecb = vecc ((λx)hati + yhatj + 4zhatk) + (yhati + xhatj + 3yhatk) = -zhati - 2zhatj - (λ + 1)xhatk` are sides of triangle as shown is figure then value of λ is 0.

Explanation:

`veca + vecb = vecc ((λx)hati + yhatj + 4zhatk) + (yhati + xhatj + 3yhatk) = -zhati - 2zhatj - (λ + 1)xhatk`

⇒ λx + y + z = 0; x + y + 2z = 0

and (λ + 1)x + 3y + 4z = 0

`|(λ, 1, 1),(1, 1, 2),((λ + 1), 3, 4)|` = 0

λ(4 – 6) – (4 – 2(λ + 1)) + (3 – (λ + 1)) = 0

–2λ – 4 + 2λ + 2 + 3 – λ – 1 = 0

–λ = 0

⇒ λ = 0