Question

Let `bar"a" = 2hat"i" + hat"j" - 2hat"k" and bar"b" = hat"i" + hat"j"`. If `bar"c"` is a vector such that `bar"a" bar"c" = |bar"c"|, |bar"c" - bar"a"| = 2sqrt2` and the angle between `bar"a" xx bar"b" and bar"c"` is 30°, then `|bar"a" xx (bar"b" xx bar"c")|` = ______.

पर्याय

• `2/3`

• `3/2`

• 2

• 3

Answer 1

Let `bar"a" = 2hat"i" + hat"j" - 2hat"k" and bar"b" = hat"i" + hat"j"`. If `bar"c"` is a vector such that `bar"a" bar"c" = |bar"c"|, |bar"c" - bar"a"| = 2sqrt2` and the angle between `bar"a" xx bar"b" and bar"c"` is 30°, then `|bar"a" xx (bar"b" xx bar"c")|` = `underline(3/2)`.

Explanation:

`|bar"c" - bar"a"| = 2sqrt2`

`=> |bar"c"|^2 + |bar"a"|^2 - 2(bar"a" * bar"c")` = 8

`=> |bar"c"|^2 + 9 - 2|bar"c"| = 8   ...[because bar"a" * bar"c" = |bar"c"| ("given")]`

`=> (|bar"c"| - 1)^2` = 0

`=> |bar"c"|` = 1

Now, 

`|bar"a" xx (bar"b" xx bar"c")| = |(bar"a" xx bar"b")||bar"c"| sin 30^circ`

`=> |bar"a" xx (bar"b" xx bar"c")| = 1/2|bar"a" xx bar"b"| = 3/2  ....[because bar"a" xx bar"b" = 2 hat"i" - 2hat"j" + hat"k"]`