Question

If `bar a = 2hat i + 3hat j - hat k`, `bar b = hat i - 4hat j + 2hat k`, find `(bar a + bar b) xx (bar a - bar b)`

Answer 1

Given: `bar a = 2hat i + 3hat j - hat k`, `bar b = hat i - 4hat j + 2hat k`

∴ `bar a + bar b = (2hat i + 3hat j - hat k) + (hat i - 4hat j + 2hat k)`

= `3hat i - hat j + hat k`

and `bar a - bar b = (2hat i + 3hat j - hat k) - (hat i - 4hat j + 2hat k)`

= `hat i + 7hat j - 3hat k`

∴ `(bar a + bar b) xx (bar a - bar b) = |(hat i, hat j, hat k),(3, -1, 1), (1, 7, -3)|`

= `(3 - 7)hat i - (- 9 - 1)hat j + (21 + 1)hat k`

= `-4hat i + 10hat j + 22hat k`.