Find the area of the parallelogram whose adjacent sides are determined by the vectors $\to a = 3^i +^j + 4^k$ and $\to b =^i -^j +^k$ .

Open in App

Solution

Area of parallelogram $= | \to a \times \to b |$
$∴ \to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 3 & 1 & 4 1 & - 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$=^i (1 + 4) -^j (3 - 4) +^k (- 3 - 1)$
$= 5^i +^j - 4^k$
$∴ | \to a \times \to b | = \sqrt{25 + 1 + 16} = \sqrt{42} =$ Area of parallelogram.

Suggest Corrections

Similar questions

\to a = 3^i +^j + 4^k

\to b =^i -^j +^k

Find the area of the parallelogram whose adjacent sides are determined by the vector .

Find the area of the parallelogram whose adjacent sides are determined by the vectors $a =^i -^j + 3^k$ and $b = 2^i - 7^j +^k$

3^i +^j - 2^k

^i - 3^j + 4^k

2^i +^j

3^i +^j + 4^k

Join BYJU'S Learning Program