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.
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