Given two vectors a- - - i - j - 2 k and b- - - i - 2 j - k-

A. #160; #160; a⃗×b⃗ = i amp; j amp; k 1 amp; 1 amp; 2 1 amp; 2 amp; 1 = 3 i 3j + 3 k Hence, the area of the triangle ...

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Standard XII

Physics

Multiplication with Vectors

Given two vec...

Question

Given two vectors $\to a = - ˆ i + ˆ j + 2 ˆ k$ and $\to b = - ˆ i - 2 ˆ j - ˆ k$ .

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Solution

a. $\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ˆ i & ˆ j & ˆ k - 1 & 1 & 2 - 1 & - 2 & - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3 ˆ i - 3 ˆ j + 3 ˆ k$
Hence, the area of the triangle is $\frac{3 \sqrt{3}}{2}$ .
b. The area of the parallelogram is $3 \sqrt{3}$
c. The area of a parallelogram whose diagonals are $2 \to a$ and $4 \to b$ is $\frac{1}{2} | 2 \to a \times 4 \to b | = 12 \sqrt{3}$
d. Volume of the parallelepiped
$= | (\to a \times \to b) \cdot \to c | = \sqrt{9 + 36 + 9} = 3 \sqrt{6}$

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Given two vectors →a=−ˆi+ˆj+2ˆk and →b=−ˆi−2ˆj−ˆk.

Given two vectors $\to a = - ˆ i + ˆ j + 2 ˆ k$ and $\to b = - ˆ i - 2 ˆ j - ˆ k$ .