Vector Algebra Test

Vector Algebra

This is Vector Algebra Test-01 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Vector has
  • A
    direction
  • B
    None of these
  • C
    magnitude
  • D
    magnitude as well as direction
    Correct
2
Position vectors of points A, B, C, etc., with respect to the origin O are generally denoted by
  • A
    \(\vec A,\;\vec B,\vec C\)
    Correct
  • B
    \(\overrightarrow {OA} ,\;\overrightarrow {OB} ,\overrightarrow {OC} \)
  • C
    \(\vec a,\;\vec b,\vec c\)
  • D
    None of these.
3
Direction angles are angles
  • A
    that show the tip of the vector
  • B
    None of these
  • C
    The angles \(\alpha ,\beta ,\gamma \) made by the position vector \(\vec r\)with the positive directions of x, y and z-axes respectively
    Correct
  • D
    The angles \(\alpha ,\beta ,\gamma \) made by the perpendicular to position vector \(\vec r\)with the positive directions of x, y and z-axes respectively
4
Direction cosines
  • A
    aresines of Direction angles
  • B
    are cosines of Direction angles
    Correct
  • C
    arecotangents of Direction angles
  • D
    are tangents of Direction angles
5
If l, m and n are direction cosines of the position vector OP the coordinates of P are
  • A
    lr, mr and n
  • B
    lr, m and nr
  • C
    l, mr and nr
  • D
    lr, mr and nr
    Correct
6
Zero Vector
  • A
    A vector whose initial points are at origin
  • B
    A vector whose terminal points are at origin
  • C
    None of these
  • D
    A vector whose initial and terminal points coincide
    Correct
7
Unit Vector is
  • A
    A vector whose magnitude is unity
    Correct
  • B
    A vector whose direction angle β is unity
  • C
    A vector whose direction angle α is unity
  • D
    A vector whose direction angle γ is unity
8
The unit vector in the direction of a given vector\(\vec a\)is denoted by
  • A
    \(\dot a\)
  • B
    \(\dddot a\)
  • C
    \(\overset{\ddot{\ }}{\mathop{a}}\,\)
  • D
    \(\hat a\)
    Correct
9
Coinitial Vectors are
  • A
    Two or more vectors having the same initial point
    Correct
  • B
    Two or more pseudo vectors having the same initial point
  • C
    Two or more vectors having the same final point
  • D
    Two or more force vectors having the same initial point
10
Vectors A and BareCollinear
  • A
    if the direction cosines of one are negatives of the other
  • B
    if they are in the same line
  • C
    if they are have equal magnitude
  • D
    if they are parallel to the same lineirrespective of their magnitudes and directions.
    Correct
11
Vectors A and B are equal
  • A
    if they have the same magnitude and direction
    Correct
  • B
    if they have the same magnitude
  • C
    if they have the same direction
  • D
    if they have the same magnitude and opposite direction
12
Negative of a Vector\(\vec a\) is a
  • A
    A vector whose magnitude is the same as that \(\vec a\)of but direction is 120°to that of \(\vec a\)
  • B
    A scalar whose magnitude is the same as that \(\vec a\)
  • C
    A vector whose magnitude is the same as that \(\vec a\)of but direction is opposite to that of \(\vec a\)
    Correct
  • D
    A vector whose magnitude is the same as that \(\vec a\)of but direction is perpendicularto that of \(\vec a\)
13
If \(\lambda \) is a real number \(\lambda \)\(\vec a\) is a
  • A
    inner product
  • B
    tensor
  • C
    scalar
  • D
    vector
    Correct
14
for vector addition which of the following is correct?
  • A
    \(\vec a + \vec b = \vec b + \vec a\) (ans)
    Correct
  • B
    |\(\vec a + \vec b\)| = \(\vec a + \vec b\)
  • C
    |\(\vec a + \vec b\)| = \(\vec a\)
  • D
    \(\overset{\ddot{\ }}{\mathop{a}}\,\)
15
for vector addition which of the following is correct?
  • A
    \(\left( {\vec a + \vec b} \right) + \vec c \geqslant \vec a + \left( {\vec b + \vec c} \right)\)
  • B
    \(\left( {\vec a + \vec b} \right) + \vec c = \vec a + \left( {\vec b + \vec c} \right)\)
    Correct
  • C
    \(\left( {\vec a + \vec b} \right) + \vec c \ne \vec a + \left( {\vec b + \vec c} \right)\)
  • D
    \(\left( {\vec a + \vec b} \right) + \vec c < \vec a + \left( {\vec b + \vec c} \right)\)