Match List-I with List-II
| List-I | List-II | ||
| (A) | Area of triangle Δ with adjacent sides $\vec{a}$ and $\vec{b}$ | (I) | $\vec{a}×\vec{b}$ |
| (B) | Area of parallelogram with adjacent side $\vec{a}×\vec{b}$ | (II) | $\frac{1}{2}|\vec{a}×\vec{b}|$ |
| (C) | $(\vec{a}-\vec{b})×(\vec{a}+\vec{b})$ | (III) | $|\vec{a}×\vec{b}|$ |
| (D) | $|\vec{a}||\vec{b}|sin \theta \hat{n}$, where symbols have their usual meaning | (IV) | $2(\vec{a}×\vec{b})$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
The correct answer is option (3) → (A)-(II),(B)-(III), (C)-(IV), (D)-(I)
(A) → $\frac{1}{2}|\vec{a}×\vec{b}|$ (II)
(B) → $|\vec{a}×\vec{b}|$ (III)
(C) $(\vec{a}-\vec{b})×(\vec{a}+\vec{b})$
$=\vec a ×\vec a+\vec a×\vec b-\vec b×\vec a-\vec b×\vec b$
$=\vec a×\vec b+\vec a×\vec b=2(\vec a×\vec b)$ (IV)
(D) $|\vec{a}||\vec{b}|\sin \theta \hat{n}=\vec a×\vec b$ (I)