What is the cross product of a vector with magnitude 18 acting in the direction of the negative x-axis and a vector of 12 acting in the z direction.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The cross product of two vectors A and B has a magnitude `|A|*|B|*sin theta` where `theta` is the angle between the vectors. The cross product of two vectors is a vector and its direction is given by the right hand rule.

Here, the first vector has a magnitude 18 and it is in the direction of the negative x-axis. The second vector has a magnitude of 12 and acts in the direction of the positive z-axis.

As the vectors are perpendicular to each other, `sin theta = sin 90 = 1` . The magnitude of the cross product is 18*12*1 = 216.

The direction of the resultant vector is in the direction of the negative y-axis.

The required cross product has a magnitude 216 and the direction of the vector is in the negative y-axis.

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