Question

Find the unit vector perpendicular to both the vectors a is 3 ICAP + 2 J cap + 2 k cap and b is 2 ICAP - 2 J cap +4 kcap

Answer 1

Answer:

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Answer 2

The vector that is perpendicular to vector A and B is $C=\dfrac{\vec{12i-8j-10j}}{17.54}$.

Explanation:

It is given that.

$A=3i+2j+2k$

$B=2i-2j+4k$

Let C is a vector that is perpendicular to vector A and B.

$C=\dfrac{\vec{C}}{|C|}$

Vector C is given by the cross product of A and B. So,

$C=A\times B$

$C=(3i+2j+2k)\times (2i-2j+4k)$

$\vec{C}=\begin{pmatrix}12&-8&-10\end{pmatrix}$

$\vec{C}=12i-8j-10j$

$|C|=\sqrt{12^2+8^2+10^2}=17.54$

So, $C=\dfrac{\vec{12i-8j-10j}}{17.54}$

So, the vector that is perpendicular to vector A and B is $C=\dfrac{\vec{12i-8j-10j}}{17.54}$. Hence, this is the required solution.

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