1. Find a unit vector which is perpendicular to both of the vectors m=[4, 2, -3] and n=[2, -3, 1]
A vector perpendicular to both m and n is the cross product. After that, you only need to normalize it to make a unit vector.
Post if you need more help.
| i j k |
| 4 2 -3 |
| 2 -3 1 |
= [-7,-10,-16]/9√5
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Correct!
thank you !
To find a unit vector that is perpendicular to both vectors m and n, you can use the cross product of the two vectors. Here's how you can do it:
1. Calculate the cross product of m and n: To find the cross product, use the following formula:
m x n = (m2 * n3 - m3 * n2) i - (m1 * n3 - m3 * n1) j + (m1 * n2 - m2 * n1) k
Using the given values, we have:
m x n = (2 * (-3) - (-3) * (-3)) i - (4 * (-3) - (-3) * 1) j + (4 * (-3) - 2 * (-3)) k
= (-6 - 9) i - (-12 - 3) j + (-12 + 6) k
= -15i - (-15)j - 6k
= -15i + 15j - 6k
2. Normalize the resulting vector: To create a unit vector, we need to normalize the resulting vector from Step 1.
To normalize the vector, divide each component of the vector by its magnitude:
magnitude = √((-15)^2 + 15^2 + (-6)^2)
= √(225 + 225 + 36)
= √486
= 3√54
Divide each component of the vector (-15, 15, -6) by the magnitude:
(-15 / (3√54), 15 / (3√54), -6 / (3√54))
Simplifying the expression:
(-5 / √54, 5 / √54, -2 / √54)
Therefore, the unit vector perpendicular to both m and n is (-5 / √54, 5 / √54, -2 / √54).