Let $\vec{a}$ be any vector such that $\vec{a}.\hat{i} = \vec{a}.(\hat{i}+\hat{j}) = \vec{a}.(\hat{i}+\hat{j}+\hat{k}) = 1$, then $\vec{a}$ is

If $|\vec{a}| = a$, then the value of $|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2$ is

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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Let $\vec{a} = \hat{i} + 4\hat{j} + 2\hat{k}$, $\vec{b} = 3\hat{i} - 2\hat{j} + 7\hat{k}$ and $\vec{c} = 2\hat{i} + \hat{j} + 4\hat{k}$. A vector $\vec{d}$ which is perpendicular to both $\vec{a}$ and $\vec{b}$, and $\vec{c} \cdot \vec{d} = 14$, is:

If $\vec{a}, \vec{b}$ and $\vec{c}$ be vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, $|\vec{a}| = 3$, $|\vec{b}| = 5$ and $|\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is

Match List - I with List - II.

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Match List-I with List-II

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