Question

Two vectors are given by 5 ˆ

i – 3 ˆ

j and 3 ˆ

i – 5 ˆ

j . Calculate their scalar and

vector products.​

Answer 1

Explanation:

as scalar product is given by A.B= AB cosx

5i-3j . 3i-5j = 15i+15j ( directly multiply the coefficients of i and j respectively)

Answer 2

Given:

A= 5iˆ- 3jˆ

B= 3iˆ- 5jˆ

solⁿ:

A.B = $\sqrt{(5X3)(-3X-5)}$

=$\sqrt{15X15}$

= 15

AxB = 15(iˆ x iˆ) - 25(iˆ x jˆ) - 9(jˆxiˆ) + 15(jˆxjˆ)

=15(0) - 25(k) - 9(-k) + 15(0)

= -25(k) + 9 (k)

= 16 (-k)

AxB is a single vector C such that |C| = 16 units  along negative z-direction.