Question

Let
A=i−2j−3k
and
B=2i+3j+k
. Find
|A×B|

(√101)

(√191)

(√195)

(√121)

Answer 1

Answer on Question #56039 – Math – Analytic Geometry

Question

Let

A=i−2j−3k

and

B=2i+3j+k.

Find

|A×B|

(√101)

(√191)

(√195)

(√121)

Solution

$$\begin{array}{l} \vec{A} \times \vec{B} = \left| \begin{array}{ccc} i & j & k \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{array} \right| = \left| \begin{array}{ccc} i & j & k \\ 1 & -2 & -3 \\ 2 & 3 & 1 \end{array} \right| = i \left| \begin{array}{ccc} -2 & -3 \\ 3 & 1 \end{array} \right| - j \left| \begin{array}{ccc} 1 & -3 \\ 2 & 1 \end{array} \right| + k \left| \begin{array}{ccc} 1 & -2 \\ 2 & 3 \end{array} \right| = \\ = i \left((-2) \cdot 1 - (-3) \cdot 3\right) - j (1 \cdot 1 - (-3) \cdot 2) + k (1 \cdot 3 - (-2) \cdot 2) \\ = i (-2 + 9) - j (1 + 6) + k (3 + 4) = (7; -7; 7) \\ \left| \vec{A} \times \vec{B} \right| = \sqrt{7^2 + (-7)^2 + 7^2} = \sqrt{147} \end{array}$$

Answer: $\sqrt{147}$

www.AssignmentExpert.com