Final answer:
The cross product of vectors a = 4j - 7k and b = -i + 3j + k is found by applying the distributive property and the cyclic order of unit vectors, yielding the result -25i + 7j - 4k.
Step-by-step explanation:
To find the cross product a x b, where vector a is given by 4j − 7k and vector b is given by −i + 3j + k, we can apply the distributive property of the cross product and the results of the cyclic order of unit vectors.
The cross product is calculated as follows:
- a x b = (4j)(−i + 3j + k) − (7k)(−i + 3j + k)
- = 4j x (−i) + 4j x 3j + 4j x k − 7k x (−i) − 7k x 3j − 7k x k
- = −4k − 0 − 4i + 7j − 21i − 0
- = −25i + 7j −4k
Thus, the cross product a x b is −25i + 7j −4k.