If vector a = 4i + 3j + 2k and vector b = 3i + 2k then find vector|b x

1.	If vector a = 4i + 3j + 2k and vector b = 3i + 2k then find vector\|b x 2a\|
Answer» We have vector a = 4i + 3j + 2k 2 vector a = 8i + 6j + 4k and vector b = 3i + 2k = 3i + 0j + 2k ∴ vector\|b x 2a\| = \|(i,j,k),(3,0,2),(8,6,4)\| = i(0 - 12) - j(12 - 16) + k(18 - 0) = -12i + 4j + 18k ∴ vector\|b x 2a\| = √(12² + 4² + 18²) = √484 = 2√121 = 22

If vector a = 4i + 3j + 2k and vector b = 3i + 2k then find vector|b x 2a|

Answer»

We have vector a = 4i + 3j + 2k

2 vector a = 8i + 6j + 4k and vector b = 3i + 2k

= 3i + 0j + 2k

∴ vector|b x 2a| = |(i,j,k),(3,0,2),(8,6,4)|

= i(0 - 12) - j(12 - 16) + k(18 - 0)

= -12i + 4j + 18k

∴ vector|b x 2a| = √(12² + 4² + 18²) = √484 = 2√121

= 22