Match List-I with List-II

Consider two vectors $\vec a =\hat i+2\hat j-\hat k$ and $\vec b = −3\hat i − 6\hat j + 3\hat k$, then

Choose the correct answer from the options given below:

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

The correct answer is Option (2) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

$\vec a=(1,2,-1),\;\vec b=(-3,-6,3)$

Since $\vec b=-3\vec a$, the vectors are opposite ⇒ angle = $\pi$.

$|\vec a|=\sqrt{6},\;|\vec b|=3\sqrt{6}$

(A) Angle between $\vec a$ and $\vec b$:

$\pi$ → (III)

(B) Angle between $\vec a$ and x–axis:

$\cos\theta=\frac{1}{\sqrt6}$ → (I)

(C) Angle between $\vec b$ and x–axis:

$\cos\theta=\frac{-1}{\sqrt6}$ → (IV)

(D) Angle between $\vec a$ and y–axis:

$\cos\theta=\frac{2}{\sqrt6}$ → (II)

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