Q. Find the sum of the vectors $\overrightarrow{a}=\hat{i}-2\hat{j}+\hat{k},\overrightarrow{b}=-2\hat{i}+4\hat{j}+5\hat{k}$ and $\overrightarrow{c}=\hat{i}-6\hat{j}-7\hat{k}$.

Q. $\overrightarrow{a}$ and $-\overrightarrow{a}$ are collinear

1. Data insufficient
2. True
3. False
4. Ambiguous

Q. Answer the following as true or false.
(i) $\overrightarrow{a}$ and $-\overrightarrow{a}$ are collinear
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.

Q. Find the direction cosines of the vector $\hat{i}+2\hat{j}+3\hat{k}$.

Q. Represent graphically a displacement of $40km$, ${30}^o$ east of north.

Q. Why were they named after the months of the year?

Q. In Figure, identify the following vectors.
(i) Coinitial
(ii) Equal
(iii) Collinear but not equal

Q. Write two different vectors having same magnitude

Q. Find the scalar and vector components of the vector with initial point $(2,1)$ and terminal point $(-5,7)$

Q. Find the values of $x$ and $y$ so that the vectors $2\hat{i}+3\hat{j}$ and $x\hat{i}+y\hat{j}$ are equal

Q. Find a vector parallel to the given vector $5\hat{i}-\hat{j}+2\hat{k}$ which has magnitude $8$ units.

Q. Two vectors having same magnitude are collinear

1. True
2. False
3. Ambiguous
4. Data insufficient

Q. Compute the magnitude of the following vectors:
$\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k};\overrightarrow{b}=2\hat{i}-7\hat{j}-3\hat{k};\overrightarrow{c}=\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k}$

Q. Find the direction cosines of the vector joining the points $A(1,2,-3)$ and $B(-1,-2,1)$ directed from $A$ to $B$.

Q. Write two different vectors having same direction

Q. Classify the following measures as scalars and vectors.
(i) $10kg$
(ii) $2metres$ north-west
(iii) ${40}^o$
(iv) $40watt$
(v) ${10}^{-19}$ coluomb
(vi) $20m/s^2$

Q. For given vectors, $\overrightarrow{a}=2\hat{i}-\hat{j}+2\hat{k}$ and $\overrightarrow{b}=-\hat{i}+\hat{j}-\hat{k}$, find the unit vector in the direction of the vector $\overrightarrow{a}+\overrightarrow{b}$

Q. Find the unit vector in the direction of vector $\overrightarrow{PQ}$, where $P$ and $Q$ are the points $(1,2,3)$ and $(4,5,6)$, respectively
Answer required

Q. Classify the following as scalar and vector quantities.
(i) Time period
(ii) Distance
(iii) Force
(iv) Velocity
(v) Work done

Q. Show that the vectors $2\hat{i}-3\hat{j}+4\hat{k}$ and $-4\hat{i}+6\hat{j}-8\hat{k}$ are collinear