Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector $\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}$ is 3,-1, 4.
(B) If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$, then their cross product is given as $\vec{a} × \vec{b}=|\vec{a}||\vec{b}| \cos \theta$
(C) The unit vector in the direction of vector $\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}$ is $\vec{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})$.
(D) If $\vec{a}=3 \hat{i}$ and $\vec{b}=4 \hat{j}$ then $\vec{a} . \vec{b}=12$.
(E) If $\vec{a}$ and $\vec{b}$ represent the adjacent sides of a triangle then its area is given of $\frac{1}{2}|\vec{a} × \vec{b}|$.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (C) and (E) only
A. True
B. False, $\vec a×\vec b=|\vec a||\vec b|\sin θ\hat n$
C. True
D. False, $\vec a.\vec b=0$
E. True