### Mathematics - Vector Algebra

#### Question - 1

If $\left| \vec { \alpha } +\vec { \beta } \right| =\left| \vec { \alpha } -\vec { \beta } \right|$,then

• A $\vec { \alpha }$ is parallel to $\beta$
• B  $\vec { \alpha }$ is perpendicular to $\vec { \beta }$
• C $\left| \overrightarrow { \alpha } \right| =\left| \overrightarrow { \beta } \right|$
• D None of these

#### Question - 2

Let P,Q,R be three points with respective position vectors i+j,i-j and ai+bj+ck.The points P,Q,R are collinear, if

• A a = b = c = 1
• B a = b = c = 0
• C a = 1,b and c arbitrary scalars
• D a and b are arbitrary scalars and c=0

#### Question - 3

If $\left| \vec { \alpha } +\vec { \beta } \right| =\left| \vec { \alpha } -\vec { \beta } \right|$then

• A $\vec { \alpha }$ is parallel to $\beta$
• B $\vec { \alpha }$ is perpendicular to `$\vec { \beta }$
• C $\left| \vec { \alpha } \right| =\left| \vec { \beta } \right|$
• D NONE OF THESE

#### Question - 4

The points with position vectors 60i+3j, 40i-8j and ai-52j are collinear, if

• A a = -40
• B a = 40
• C a = 20
• D NONE OF THESE

#### Question - 5

The two vectors $\vec { a } \quad and\quad \vec { b }$ given as $\vec { a } =2i+j+3k,\quad \vec { a } =4i-\lambda j+6k$ are parallel if

• A $\lambda \quad =\quad 2$
• B $\lambda \quad =\quad -3$
• C $\lambda \quad =\quad 3$
• D $\lambda \quad =\quad -2$

#### Question - 6

Let P, Q, R be three points with respective position vectors i+j, i-j and ai+bj+ck. The points P, Q, R are collinear, if

• A a = b = c = 1
• B a = b = c = 0
• C a = 1, b and c arbitrary scalars
• D a and b are arbitrary scalars and c = 0.

#### Question - 7

The system of vector is

• A closed under addition only
• B closed under multiplication only
• C closed under addition and multiplication
• D None of these

#### Question - 8

The value of $\lambda$ such that $(x,y,z)\quad \neq \quad (0,0,0)$ and (i+j+3k)x + (3i-3j+k)y + (-4i+5j)z = $\lambda$(ix+jy+kz) are

• A 0,1
• B 0,-1
• C -1,1
• D NONE OF THESE

#### Question - 9

If $\vec { a } \quad and\quad \vec { b }$ are two non-collinear vectors and $\vec { r }$ is a vector coplanar with $\vec { a } \quad and\quad \vec { b }$ then

• A $\vec { r } \quad =\quad \vec { a } +\vec { b }$
• B $\vec { r } \quad =\quad \vec { a } -\vec { b }$
• C $r\quad =\quad m\vec { a } +\quad m\vec { b }$
• D NONE OF THESE

#### Question - 10

The position vectors of points A, B, C are i+j+k, i+2j+3k and 2i-j+k. The $\triangle ABC$ is

• A an isoceles triangle
• B an equilateral triangle
• C a scalene triangle
• D a right angled triangle.