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vova2212 [387]
3 years ago
13

Given two vectors a⃗ =−2.00i^+3.00j^+4.00k^ and b⃗ =3.00i^+1.00j^−3.00k^. Obtain a unit vector perpendicular to these two vector

s. Express your answer as a unit vector n^ in the form nx, ny, nz where the x, y, and z components are separated by commas.
Mathematics
1 answer:
Illusion [34]3 years ago
6 0

we are given two vectors as

a=-2i+3j+4k

b=3i+1j-3k

now, we can find cross product

aXb=(-2i+3j+4k)X(3i+1j-3k)

=\begin{pmatrix}3\left(-3\right)-4\times \:1&4\times \:3-\left(-2\left(-3\right)\right)&-2\times \:1-3\times \:3\end{pmatrix}

aXb=-13i+6j-11k

|aXb|=\sqrt{(-13)^2+(6)^2+(-11)^2}

|aXb|=\sqrt{326}

now, we can find normal unit vector

n=\frac{aXb}{|aXb|}

now, we can plug values

n=\frac{(-13i+6j-11k)}{\sqrt{326}}

n=\frac{-13}{\sqrt{326}}i+\frac{6}{\sqrt{326}}j-\frac{11}{\sqrt{326}}k

now, we can find components

n_x=\frac{-13}{\sqrt{326}},n_y=\frac{6}{\sqrt{326}}j,n_z=-\frac{11}{\sqrt{326}}

...............Answer

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