Question

Which of the following is a unit vector perpendicular to the plane determined by the vectors a = 2i + 4j and b = i + j - k?

1) i + 2j - 2k
2) i - 2j + 2k
3) 2i + j - k
4) 2i - j + k

Answer 1

To find a unit vector perpendicular to the given plane, we can find the cross product of the two given vectors and normalize it to a unit vector.

Step-by-step explanation:

To find a unit vector perpendicular to the plane determined by the vectors a = 2i + 4j and b = i + j - k, we can use the cross product. The cross product of two vectors gives a vector that is perpendicular to both of the original vectors. In this case, the cross product of a and b is (-5i + 7k). To make it a unit vector, we divide it by its magnitude:

(-5i + 7k) / √(52 + 02 + 72) = (-5i + 7k) / √(74) = (-(5/√(74))i + (7/√(74))k).