Suppose a→=2i+4j+3k and b→=i+5j-2k, then the vector product is ________
To find the vector product (also known as the cross product) of two vectors, we can use the formula:
a→ x b→ = (a2b3 - a3b2)i + (a3b1 - a1b3)j + (a1b2 - a2b1)k
where a→ = ai + bj + ck is the first vector, and b→ = di + ej + fk is the second vector.
Given a→ = 2i + 4j + 3k and b→ = i + 5j - 2k, we can substitute the values into the formula:
a→ x b→ = (2 * (-2) - 3 * 5)i + (3 * 1 - 2 * 2)j + (2 * 5 - 4 * 1)k
= (-4 - 15)i + (3 - 4)j + (10 - 4)k
= -19i - 1j + 6k
Therefore, the vector product of a→ and b→ is -19i - j + 6k.