Question

If `bar"a" = 3hat"i" - 2hat"j" + 7hat"k", bar"b" = 5hat"i" + hat"j" - 2hat"k"` and `bar "c" = hat"i" + hat"j" - hat"k"`, then `[bar"a"  bar"b"  bar"c"]` = ______.

Options

• 15

• 20

• 25

• 30

Answer 1

If `bar"a" = 3hat"i" - 2hat"j" + 7hat"k", bar"b" = 5hat"i" + hat"j" - 2hat"k"` and `bar "c" = hat"i" + hat"j" - hat"k"`, then `[bar"a"  bar"b"  bar"c"]` = 25.

Explanation:

`[bar"a"  bar"b"  bar"c"] = |(3,-2,7),(5,1,-2),(1,1,-1)|`

= 3(- 1 + 2) + 2(- 5 + 2) + 7(5 - 1)

= 25