Collinear Vectors

Q. The three points whose position vectors are $\hat{i}+2\hat{j}+3\hat{k},3\hat{i}+4\hat{j}+7\hat{k}and-3\hat{i}-2\hat{j}-5\hat{k}$

1. form the vertices of an equilateral triangle
2. form the vertices of a right angled triangle
3. are collinear
4. form the vertices of an isosceles triangle.

Q.

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three non-zero vectors, no two of which are collinear, $\overrightarrow{a}+\overrightarrow{b}$ is collinear with $\overrightarrow{c}$ and $\overrightarrow{b}+3\overrightarrow{c}$ is collinear with $\overrightarrow{a}$, then $|\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}|$ will be equal to

1. zero

2. 1

3. 9

4. 4

Q.

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three non -zero vectors such that they are mutually non collinear. If the vector $\overrightarrow{a}+2\overrightarrow{b}$ is collinear with $\overrightarrow{c}$ and $\overrightarrow{b}+3\overrightarrow{c}$ is collinear with $\overrightarrow{a}$ then $\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}$ equals

1. $\lambda \overrightarrow{a}$$(\lambda$ being some non -zero scalar)

2. $\lambda \overrightarrow{b}$$(\lambda$ being some non -zero scalar)

3. $\lambda \overrightarrow{c}$$(\lambda$ being some non -zero scalar)

4. $0$

Q. Collinear vectors need to have same direction

1. True
2. False

Q.

The points with position vectors $60\hat{i}+3\hat{j},40\hat{i}-8\hat{j},a\hat{i}-52\hat{j}$ are collinear, if

1. a = -40

2. a = 40

3. a = 20

4. a= -20