Determine (`bar6i`+`bar2j`) · (`bari` - `bar4j` + `bark`)

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to multiply each term in sum `6 bari + 2 barj`  by the brackets `bar i - 4 bar j + bar k`  such that:

`6 bar i(bar i - 4 bar j + bar k) + 2bar j(bar i - 4 bar j + bar k)`

`6bar i*bar i - 24 bar i*bar j + 6 bar i*bar k + 2 bar j*bar i - 8 bar j*bar j + 2 bar j* bar k`

You need to remember that cross products of different unit vectors `bar i*bar j ` , `bar i*bar k, bar j* bar k`  yield zeroes since the unit vector are orthogonal, hence:

`6bar i*bar i - 24 bar i*bar j + 6 bar i*bar k + 2 bar j*bar i - 8 bar j*bar j + 2 bar j* bar k = 6(bar i)^2 - 8(bar j)^2`

You need to remember that cross products of like unit vectors `bar i*bar i = 1`  and `bar j*bar j = 1` .

`6bar i*bar i - 24 bar i*bar j + 6 bar i*bar k + 2 bar j*bar i - 8 bar j*bar j + 2 bar j* bar k = 6 - 8 = -2`

Hence, multiplying the vectors `6 bari + 2 barj ` and `bar i - 4 bar j + bar k`  yields -2.

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question