Question

Determine λ, for which the volume of the parallelepiped having coterminous edges i + j, 3i - j and 3j + λk is 16 cubic units.

Answer 1

Answer:

λ = -4

Step-by-step explanation:

To find the value of $\lambda$ of the parallelepiped having coterminous edges  

$\vec a = \hat i+\hat j\\ \\\vec b = 3\hat i-\hat j\\\\\vec c =3\hat j+\lambda \hat k$

and volume 16 cubic units.

we have to calculate Scalar triplet ,and equate with given volume in order to find λ.

$[\vec a\:\:\:\vec b\:\:\:\vec c]=\vec a.(\vec b\times \vec c)\\\\for\\\\(\vec b\times \vec c)=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-1&0\\0&3&\lambda \end{array}\right| \\\\=\hat i (-\lambda-0)-\hat j (3\lambda-0)+\hat k (9)\\\\=-\lambda \hat i-3\lambda\hat j+9\:\hat k$

$\vec a.(\vec b \times \vec c)=(\hat i+\hat j).(-\lambda \hat i-3\lambda\hat j+9\:\hat k)=16\\\\-\lambda-3\lambda=16\\\\-4\lambda =16\\\\\lambda =-4$

Answer 2

Answer:

please see the above attachment.....