If `|vec(c)|=10, |vec(b)|=2 and vec(a)*vec(b)=12`, then what is the value of `|vec(a)xxvec(b)|`?

Options

A. 12
B. 16
C. 20
D. 24

Answer

B

Explanation

We have
`cos theta = (vec(a).vec(b))/(|vec(a)||vec(b)|) and sin theta = (|vec(a)xx vec (b)|)/(|vec(a)||vec(b)|)`
Given, `|vec(a)|=10, |vec(b)|=2, vec(a).vec(b)=12`
`:.cos theta = (12)/(20) and sin theta = (|vec(a)xxvec(b)|)/(20)`
Now, By squaring and adding , we get
`sin^(2) theta + cos^(2) theta = 1`
`rArr (|vec(a)xx vec(b)|^(2))/(400)+(144)/(400)=1 rArr |vec(a)xx vec(b)|^(2)=256`
`rArr |vec(a)xx vec(b)|=16`