Collinear Vectors

Q. 34. The magnitude of the sum of two vector is equal to the difference of their magnitude.what is the angle between s vector s?

Q.

The general values of $\theta$ satisfying the equation $2{\sin }^2\theta -3\sin \theta -2=0$ is

1. $n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\frac{\mathrm{\pi }}{6}$

2. $n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\frac{\mathrm{\pi }}{2}$

3. $n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\frac{5\mathrm{\pi }}{6}$

4. $n\mathrm{\pi }+{(-1)}^{\mathrm{n}}\frac{7\mathrm{\pi }}{6}$

Q.

Let $a$, $b$ and $c$ be three non - zero vectors such that no two of these are collinear. If the vector $a+2b$ is collinear with $c$, $b+3c$ is collinear with $a$ then $a+2b+6c$ is equals to

1. $\lambda a(\lambda \ne 0,\text{a}\text{scalar})$

2. $\lambda b(\lambda \ne 0,\text{a scalar})$

3. $\lambda c(\lambda \ne 0,\text{a}\text{scalar})$

4. $0$

Q. If an angle between vectors a and b is 120^° and |a|=3 and |b|=4 then length of vector (4a-3b) will be

Q. Answer the following as true or false:
(i) Two collinear vectors having the same magnitude are equal.

Q. If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non coplanar vectors, then
$[\overrightarrow{a}\times \overrightarrow{b},\overrightarrow{b}\times \overrightarrow{c},\overrightarrow{c}\times \overrightarrow{a}]$is equal to

1. $0$
2. $[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}{]}^2$
3. $\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]$
4. $2\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]$

Q.

Answer the following as true or false:
(i) a and -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. Collinear vectors need to have same direction

1. True
2. False

Q. 1. If a , b , c be three non coplanar vectors and r be any arbitrary vector , then (ab)(rc)+(bc)(ra)+(ca)(rb) is equal to

Q.

Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1) are collinear.

Q.

The points $A(x_1,y_1),B(x_2,y_2)$ and $C(x_3,y_3)$ are the vertices of $ABC$. (ii) Find the coordinates of the point $P$ on $AD$ such that $AP:PD=2:1$.

Q. The values of $x$ for which the angle between the vectors $\overrightarrow{a}=x\hat{i}-3\hat{j}-\hat{k}$ and $\overrightarrow{b}=2x\hat{i}+x\hat{j}-\hat{k}$ is acute and the angle between the vector $\overrightarrow{b}$ and the axis of ordinates is obtuse, are

1. $\{1,2\}$
2. $\{-2,-3\}$
3. $(-\infty ,0)$
4. $(0,\infty )$

Q.

If ${\mathrm{t}}_1,{\mathrm{t}}_2,{\mathrm{t}}_3$ are distinct and the points $\left({\mathrm{t}}_1,2{\mathrm{at}}_1+{{\mathrm{at}}_1}^3\right),\left({\mathrm{t}}_2,2{\mathrm{at}}_2+{{\mathrm{at}}_2}^3\right),\left({\mathrm{t}}_3,2{\mathrm{at}}_3+{{\mathrm{at}}_3}^3\right)$ are collinear then find the value of ${\mathrm{t}}_1+\hspace{0.17em}{\mathrm{t}}_2+{\mathrm{t}}_3$ .

Q. Answer the following as true or false:
(i) Two collinear vectors are always equal in magnitude.

Q. If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are three unit vectors equally inclined to each, then the maximum angle between vectors is

1. $\frac{\pi }{2}$
2. $\frac{\pi }{3}$
3. $\frac{2\pi }{3}$
4. $\frac{5\pi }{3}$

Q. If vectors A and B have an angle thitha between the value of |A(cap)-BCAP(cap)| will be

Q. Show that the points representing the complex numbers (3+3i), (-3-3i) and $(-3\sqrt{3}+3\sqrt{3}i)$ on the Argand plane are the vertices of an equilateral triangle.

Q. The image of the point $(1,3,4)$ with respect to the $xz$-plane is

1. $(-1,3,4)$
2. $(1,-3,4)$
3. $(-1,-3,-4)$
4. $(-1,3,-4)$

Q.

If $\mathrm{f}\left(\mathrm{x}\right)=10\cos \mathrm{x}+(13+2\mathrm{x})\sin \mathrm{x}$, then $f"\left(x\right)+f\left(x\right)$ is equal to

1. $\cos x$

2. $4\cos x$

3. $\sin x$

4. $4\sin x$

Q.

One possible condition for the three points $(\mathrm{a},\mathrm{b}),(\mathrm{b},\mathrm{a})$ and $({\mathrm{a}}^2,-{\mathrm{b}}^2)$ to be collinear, is

1. $\mathrm{a}–\mathrm{b}=2$

2. $\mathrm{a}+\mathrm{b}=2$

3. $\mathrm{a}=1+\mathrm{b}$

4. $\mathrm{a}=\; 1\; –\mathrm{b}$

Q.

Vectors that may be subject to its parallel displacement without changing its magnitude and direction are called _________.

1. Free vectors

2. Parallel vectors.

3. Coinitial vectors

4. Collinear vectors.

Q. Sides of triangle $ABC$ are in $A.P.$ If $a<min\{b,c\},$ then $\cos A$ may be equal to:

1. $\frac{5b-3a}{7b}$
2. $\frac{4c-3b}{2c}$
3. $\frac{5a-3b}{7a}$
4. $\frac{4b-3c}{2b}$

Q. 19. If vector a b c and d are non coplanar vectors , then d.{ax[bx(cxd)]} is equal to ?

Q. 16. Three vectors A, B and C are related as A +B=C. If vector C is perpendicular to vector A and the magnitude of C is equal to the magnitude of A what will be the angle between vectors A and B

Q. If the points A, B and C have position vectors (2, 1, 1), (6, -1, 2) and (14, P) respectively and if they are collinear, then P =

1. 2
2. 4
3. 6
4. 8

Q. Answer the following as true or false. (i) and 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. If in a $△ABC$, the side $c$ and the angle $C$ remain constant, while the remaining elements are changed slightly, then the value of $\frac{da}{\cos A}+\frac{db}{\cos B}$ is

Q. Answer the following as true or false:
(i) Two vectors having same magnitude are collinear.

Q. 6. For non zero vectors a, b, c ; magnitude of axb.c = magnitude of a, b, c holds only if ?

Q.

There are $18$ points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is :

1. $816$

2. $806$

3. $805$

4. $813$