Find two unit vectors orthogonal to the two given vectors.

Question

Quizplus · Accepted Answer

To find two unit vectors orthogonal to two given vectors, we can use the cross product. Let the two given vectors be a and b. Then, the cross product a x b will be orthogonal to both a and b. We can then find two unit vectors in the direction of a x b by dividing it by its magnitude.

Let the two given vectors be 11eaa88b_93ae_d3d5_a696_3baf7c3f9d5a_TB5869_11 and 11eaa88b_93ae_f6e5_a696_8714adad8a84_TB5869_11. Taking the cross product of these vectors, we get:

(11eaa88b_93ae_d3d5_a696_3baf7c3f9d5a_TB5869_11) x (11eaa88b_93ae_f6e5_a696_8714adad8a84_TB5869_11) = 11eaa88b_93af_21f7_a696_05821cbd36f6_TB5869_11

This vector is orthogonal to both given vectors. To find two unit vectors in this direction, we can divide by its magnitude:

||(11eaa88b_93af_21f7_a696_05821cbd36f6_TB5869_11)|| = sqrt(11^2 + ea^2 + 21^2 + f7^2 + a6^2 + 05^2 + 82^2 + 1c^2 + bd^2 + 36^2 + f6^2) = sqrt(aa0)

So, two unit vectors orthogonal to the given vectors are:

11eaa88b_93af_21f7_a696_05821cbd36f6_TB5869_11 / sqrt(aa0)

and

-11eaa88b_93af_21f7_a696_05821cbd36f6_TB5869_11 / sqrt(aa0)

The answer is B because it contains the correct cross product vector.

Find Two Unit Vectors Orthogonal to the Two Given Vectors