Question

A=2i-3j+7k,b= i+2k,c=j-k find a.b×c​

Answer 1

The value of
`a\cdot b* c` is 0.

Step-by-step explanation:

The three vectors provided are:

`a=2i-3j+7k\\b= i+2k\\c=j-k`

The value to be computed is:

`a\cdot b* c`

Compute the value of (b × c) as follows:

`b* c=\left|\begin{array}{ccc}i&j&k\\1&0&2\\0&1&-1\end{array}\right|`

`=\left|\begin{array}{cc}0&2\\1&-1\end{array}\right|i-\left|\begin{array}{cc}1&2\\0&-1\end{array}\right|j+\left|\begin{array}{cc}1&0\\0&1\end{array}\right|k\\\\=-2i+1j+1k`

Now compute the value of
`a\cdot b* c` as follows:

`a\cdot b* c=(2i-3j+7k)\cdot (-2i+j+k)`

`=(2\cdot -2)+(-3\cdot 1)+(7\cdot1)\\\\=-4-3+7\\\\=0`

Thus, the value of
`a\cdot b* c` is 0.