Multiplication of a Vector by a Scalar

Q.

Which of the following is true about multiplication of a vector by a scalar.

1) Scalar multiplication by a positive number other than 1 changes its magnitude but not direction.

2) Scalar multiplication always lead to change in magnitude and direction.

3) Scalar multiplication by -1 will not change the magnitude of the vector but will change its direction.

4) Scalar multiplication by a negative number other than -1 will reverse its direction and change its magnitude as well.

1. All are correct

2. 1 and 4 are correct

3. 1, 3 and 4 are correct

4. 2, 3 and 4 are correct

Q. If p = (3, 5), then 2p, -4p and $\frac{1}{3}$ p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

Q. If $\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k}$, then the vector in the direction of $\overrightarrow{a}$ and having magnitude as $|\overrightarrow{b}|$, is

1. $7(\hat{i}+2\hat{j}+2\hat{k})$
2. $\frac{7}{9}(\hat{i}+2\hat{j}+2\hat{k})$
3. $\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$
4. $Noneofthese$