Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Area of triangle determined by vectors $(\hat{i}+\hat{j})$ and $(\hat{i}-2\hat{j}+\hat{k})$ is	I. 0
B. The value of $(\hat{i}\times\hat{j}).\hat{j} + (\hat{j}\times\hat{i}).\hat{k} + (\hat{k}\times\hat{i}).\hat{j}$ is	II. $\dfrac{\sqrt{11}}{2}$
C. If $(2\lambda-1)\hat{i}+3\hat{j}-\hat{k}$ and $\hat{i}+\lambda\hat{j}+2\hat{k}$ are perpendicular to each other then $\lambda$ is	III. 4
D. Projection of $5\hat{i}+\hat{j}+4\hat{k}$ on $2\hat{i}+6\hat{j}+3\hat{k}$ is	IV. 3/5

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Which of the following statement are true?

A. The angle between the vectors $2\hat i+\hat j+3\hat k$ and $3\hat i-2\hat k$ is $\frac{\pi}{2}$

B. If $\vec a$ and $\vec b$ are two non-zero vectors, then projection of $\vec b$ on $\vec a$ is $\frac{\vec a\cdot\vec b}{|\vec a|}$

C. The unit vector normal to both vectors $\vec a=\hat i-\hat j-\hat k$ and $\vec b=\hat i+\hat j+\hat k$ is $\frac{1}{\sqrt2}(-\hat j+\hat k)$

D. The area of triangle formed by adjacent sides represented by vectors $\vec a=3\hat i+4\hat j$ and $\vec b=-5\hat i+7\hat j$ is 41 sq. units

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Given that $\vec{a} = -3\hat{i} - 6\hat{j} + 4\hat{k}$, $\vec{b} = 9\hat{i} - λ\hat{j} - 12\hat{k}$. If $\vec{a} \times \vec{b} = \vec{0}$, then the value of λ is

Which of the following cannot be the direction ratios of the straight line $\frac{x-3}{2}=\frac{2-y}{3}=\frac{z+4}{-1}$ ?

let $\vec{a}$ be a non-zero vector of magnitude '$a$' and $\lambda$ is a non-zero scalar, then $\lambda\vec{a}$ is a unit vector if

The angle between the vectors $\hat{i} - \hat{j}$ and $\hat{j} - \hat{k}$ is:

If $\vec a, \vec b$ and $\vec c$ are vectors such that $|\vec a|=5, |\vec b|=12, |\vec c|=13$ and $\vec a+\vec b+\vec c=\vec 0$, then

Match List-I with List-II

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