1.IF Vector OA =2i + 3j – k, vectorOB = i – 2j + 3k determine the value of vectorS ,OA X OB

To determine the value of the vector product (also known as the cross product) of vectors OA and OB, denoted as OA x OB, we can use the following formula:

OA x OB = (OA_y * OB_z - OA_z * OB_y) i + (OA_z * OB_x - OA_x * OB_z) j + (OA_x * OB_y - OA_y * OB_x) k

Now, let's substitute the given vector values into the formula:

OA = 2i + 3j - k
OB = i - 2j + 3k

By substituting these values into the formula, we get:

OA x OB = ((3*(-2)) - ((-1)*(-2)))i + (((-1)*3) - (2*2))j + ((2*(-2)) - (3*1))k

Simplifying further, we have:

OA x OB = (-6 + 2)i + (-3 - 4)j + (-4 - 3)k
= -4i - 7j - 7k

Therefore, the value of vector S, which is equal to OA x OB, is:

vector S = -4i - 7j - 7k