# Given two vectors find a unit vector that is perpendicular

Given two vectors \vec{A} = - 2.00 \hat{ i } + 3.00 \hat{ j } + 4.00 \hat{k} and \vec{B} = 3.00 \hat{ i } + 1.00 \hat{ j } - 3.00 \hat{k}. Obtain a unit vector perpendicular to these two vectors.

Express your answer as a unit vector N_unit in the form N_x, N_y, N_z where the x, y, and z components are separated by commas.

i know this involves the cross product but im stuck on what to do, can someone help me please?

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ehild
Homework Helper
Fist calculate the cross product of the two vectors

$$\vec{A} = - 2.00 \hat{ i } + 3.00 \hat{ j } + 4.00 \hat{k}$$

and

$$\vec{B} = 3.00 \hat{ i } + 1.00 \hat{ j } - 3.00 \hat{k}$$

ehild

i get -13, 6, -11, if my calculations are correct. do i need to find the magnitude of this? sqrt of 326... hen divide by this amount for each. Do I also need to change the +/- signs to make it perpendicular

Last edited:
ehild
Homework Helper
The vector product is correct. The magnitude is correct. Yes, divide each component with the magnitude. You can use the signs as they are or change all to opposite, the vector stays perpendicular.

ehild

ty so much for your help