(a) Find the cross product of the two vectors overrightarrow (A)=8overrightarrow (i)+3overrightarrow (j) and overrightarrow (B)=-5overrightarrow (i)-7overrightarrow (j) (b) Verify explicitly that overrightarrow (A)times overrightarrow (B)=-overrightarrow (B)times overrightarrow (A)

Question

Answer 1

(a) To find the cross product of two vectors

and

, we use the determinant of a matrix formed by the unit vectors

and

, and the components of the vectors

and

. The cross product is given by:

Expanding the determinant, we get:

Simplifying the expression, we have:

Therefore, the cross product of

and

is

.(b) To verify that

, we need to find the cross product of

and

and compare it with

.

Expanding the determinant, we get:

Simplifying the expression, we have:

Now, let's compare it with

:

We can see that

, which verifies the given statement.

Soru