Question

Find a vector perpendicularto both i+j and i-2k .

Short answer

The vector perpendicular to both the given vectors i+j and i-2k is -2i+2j-k .

Step-by-step solution

Given information

The given vectors are i+j and i$-$2k.

Formula used to find a vector perpendicular to the two vectors.

The formula used to find the vector perpendicular to the two vectors and is given by

A xB =$\left[\begin{array}{ccc}i& j& k\\ Ax& Ay& Az\\ Bx& By& Bz\end{array}\right]$

Substitute the values

Let the given vectors be A = i+j and B = i - 2k .

A x B = $\left|\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ 1& 1& 0\\ 1& 0& -2\end{array}\right|$

= i(-2-0) - j(-2-0) + k(0-1)

= i(-2) - j(-2) + k(-1)

= -2i+2j-k

Hence, the vector perpendicular to A = i+j and B = i$-$2k is .