Collinear Vectors

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.
The vector having magnitude of 12 units in the direction of the $\overrightarrow{A}=3\hat{i}+2\hat{j}-6\hat{k}$
is

1. $36\hat{i}+24\hat{j}-72\hat{k}$
2. $\frac{(36\hat{i}+24\hat{j}-72\hat{k})}{7}$
3. $12\hat{i}+12\hat{j}-12\hat{k}$
4. $\frac{(3\hat{i}+2\hat{j}-6\hat{k})}{7}$

Q. Let a, b and c be three nonzero vectors, no two of which are collinear. If the vector a+2b is collinear with c, and b+3c is collinear with a, then a+2b+6c =

1. $\lambda a$
2. $\lambda b$
3. $\lambda c$
4. $0$

Q. If $\overrightarrow{a}\times \overrightarrow{b}$ is defined as $\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|$ $\sin \theta$ where $\theta$ is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ and it is given that $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear vectors, then $\overrightarrow{a}\times \overrightarrow{b}$ =;___

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 $\overrightarrow{a}\times \overrightarrow{b}$ is defined as $\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|$ $\sin \theta$ where $\theta$ is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ and it is given that $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear vectors, then $\overrightarrow{a}\times \overrightarrow{b}$ =;___

Q. Which of the following vectors are parallel to the vector $i+j$ ?

1. i-j
2. -2i-2j
3. 5i+5j
4. i+2j
5. 3i+j
6. -3i+3j
7. i-2j
8. 3i+3j
9. -9i-9j
10. 6i+6j

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.

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