Vector Algebra

The non-adjacent vertex in the graph is

Let $\vec{a}=2\hat{i}-\hat{j}+2\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-\hat{k}.$Let a vector $\vec{v}$ be in the plane containing $\vec{a}$ and $\vec{b}.$If $\vec{v}$ is perpendicular to the vector…

What is the scalar projection of $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$ on $\vec{b}=4 \hat{i}-4 \hat{j}+7 \hat{k}$ ?

If the position vectors of $A$ and $B$ are $(\sqrt{2}-1) \hat{i}-\hat{j}$ and $\hat{i}+(\sqrt{2}+1) \hat{j}$ respectively, then what is the magnitude of $\overrightarrow{\mathrm{AB}}$ ?

If are the position vectors of the vertices $A, B, C$ respectively of a triangle $A B C$ and $G$ is the centroid of the triangle, then what is equal to?

If $|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$, then which one of the following is correct?

If $|\vec{a}|=2$ and $|\vec{b}|=3$, then $|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2$ is equal to

The vector $\vec{a}$ lies in the plane of vectors $\vec{b}$ and $\vec{c}$. Which one of the following is correct?

Which one of the following vectors is normal to the vector $\hat{i}+\hat{j}+\hat{k}$ ?

Consider the following : $4 \hat{i} \times 3 \hat{i}=\overrightarrow{0}$ $\frac{4 \hat{i}}{3 \hat{i}}=\frac{4}{3}$ Which of the above is/are correct?

Let $p, q, r, s$ be respectively the magnitudes of the vectors $3 \hat{i}-2 \hat{j}, 2 \hat{i}+2 \hat{j}+\hat{k}, 4 \hat{i}-\hat{j}+\hat{k}, \quad 2 \hat{i}+2 \hat{j}+3 \hat{k}$. Which one of the following is correct?

What is the value of $p$ for which the vector $p(2 \hat{i}-\hat{j}+2 \hat{k})$ is of 3 units length?