Question

Let `veca = 2hati + hatj - 2hatk` and `vecb = hati + hatj`. If `vecc` is a vector such that `veca.vecc = |vecc|, |vecc - veca| = 2sqrt(2)`, angle between `(veca xx vecb)` and `vecc` is `π/6`, then the value of `|(veca xx vecb) xx vecc|` is ______.

विकल्प

• `2/3`

• 4

• 3

• `3/2`

Answer 1

Let `veca = 2hati + hatj - 2hatk` and `vecb = hati + hatj`. If `vecc` is a vector such that `veca.vecc = |vecc|, |vecc - veca| = 2sqrt(2)`, angle between `(veca xx vecb)` and `vecc` is `π/6`, then the value of `|(veca xx vecb) xx vecc|` is `underlinebb(3/2)`.

Explanation:

`veca xx vecb = |(hati, hatj, hatk),(2, 1, -2),(1, 1, 0)| = i(2) – j(2) + k(1) = 2hati - 2hatj + hatk`

∴ `|veca xx vecb|` = 3

Now, `|vecc - veca|^2` = 8

⇒ `|vecc|^2 + |veca|^2 - 2veca.vecc` = 8

⇒ `|vecc|^2 + 9 - 2|vecc|` = 8  ...`[∵ |veca|^2 = 2^2 + 1^2 + (-2)^2 = 9]`

⇒ `|vecc| - 2|vecc|^2 + 1` = 0

⇒ `|vecc|` = 1

Now, `|(veca xx vecb) xx vecc| = |veca xx vecb||vecc|sin(π/6) = 3 xx 1 xx 1/2`

⇒ `|(veca xx vecb) xx vecc| = 3/2`