Question

Evaluate
(2i−4k)×(i+2j)

8i−4j+4k

2i+4j+3k

3i+4j+2k

5i−3j−k

Answer 1

Answer on Question #56037 – Math – Analytic Geometry

Evaluate $(2i - 4k) \times (i + 2j)$.

a) $8i - 4j + 4k$

b) $2i + 4j + 3k$

c) $3i + 4j + 2k$

d) $5i - 3j - k$

Solution

The cross (vector) product can be rewritten in the following form:

$$(2i - 4k) \times (i + 2j) = \begin{vmatrix} i & j & k \\ 2 & 0 & -4 \\ 1 & 2 & 0 \end{vmatrix} = i \begin{vmatrix} 0 & -4 \\ 2 & 0 \end{vmatrix} - j \begin{vmatrix} 2 & -4 \\ 1 & 0 \end{vmatrix} + k \begin{vmatrix} 2 & 0 \\ 1 & 2 \end{vmatrix} = \\ = 8i - 4j + 4k.$$

Answer: $(2i - 4k) \times (i + 2j) = 8i - 4j + 4k.$

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