Let be the angle between two vectors a and b. Then match List-I with List-II | List-I | List-II | | --- | --- | | (A) | (I) a * b a b | | (B) | (II) a x b | | (C) Area of the parallelogram with adjacent sides represented by a and b | (III) a * b a | | (D) Projection of a on b | (IV) a x b a b | Choose the correct answer from the options given below: Option 1: (A) - (IV), (B) - (I), (C) - (II), (D) - (III) Option 2: (A) - (I), (B) - (IV), (C) - (II), (D) - (III) Option 3: (A) - (IV), (B) - (I), (C) - (III), (D) - (II) Option 4: (A) - (I), (B) - (IV), (C) - (III), (D) - (II)

The answer is '(A) - (IV), (B) - (I), (C) - (II), (D) - (III)'. View full solution:

Algebra > Vector Algebra

Medium

core

Let $\theta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$. Then match List-I with List-II | List-I | List-II | | --- | --- | | (A) $\sin \theta$ | (I) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert \vert \vec{b}\vert }$ | | (B) $\cos \theta$ | (II) $\vert \vec{a} \times \vec{b}\vert $ | | (C) Area of the parallelogram with adjacent sides represented by $\vec{a}$ and $\vec{b}$ | (III) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert }$ | | (D) Projection of $\vec{a}$ on $\vec{b}$ | (IV) $\dfrac{\vert \vec{a} \times \vec{b}\vert }{\vert \vec{a}\vert \vert \vec{b}\vert }$ | Choose the correct answer from the options given below:

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

(A) - (I), (B) - (IV), (C) - (II), (D) - (III)

(A) - (IV), (B) - (I), (C) - (III), (D) - (II)

(A) - (I), (B) - (IV), (C) - (III), (D) - (II)

✅ Correct Option: 1

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