Vector Algebra Test

Vector Algebra

This is Vector Algebra Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Correct form of distributive law is
  • A
    \(k\vec a + m\vec a \ll \left( {k + m} \right)\vec a\)
  • B
    \(k\vec a + m\vec a > \left( {k + m} \right)\vec a\)
  • C
    \(k\vec a + m\vec a \ne \left( {k + m} \right)\vec a\)
  • D
    \(k\vec a + m\vec a = \left( {k + m} \right)\vec a\)
    Correct
2
If \({P_1}\left( {{x_1},{\text{ }}{y_1},{\text{ }}{z_1}} \right)\) and \({P_2}\left( {{x_2},{\text{ }}{y_2},{\text{ }}{z_2}} \right)\) are any two points, then the vector joining P1 and P2is the vector P1P2. Magnitude of the vector \(\overrightarrow {{P_1}{P_2}} \) is
  • A
    \(\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \)
    Correct
  • B
    \(\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} + {z_1}} \right)}^2}} \)
  • C
    \(\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} + {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \)
  • D
    \(\sqrt {{{\left( {{x_2} + {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \)
3
If \(\vec a,\;\vec b\;and\;\vec c\) are any three vectors then the correct expression for distributivity of scalar product over addition is
  • A
    \(\vec a.\left( {\vec b + \vec c} \right) < \vec a.\vec b + \vec a.\vec c\)
  • B
    \(\vec a.\left( {\vec b + \vec c} \right) = \vec a.\vec b + \vec a.\vec c\)
    Correct
  • C
    \(\vec a.\left( {\vec b + \vec c} \right) \ne \vec a.\vec b + \vec a.\vec c\)
  • D
    \(\vec a.\left( {\vec b + \vec c} \right)\;\~\;\vec a.\vec b + \vec a.\vec c\)
4
Magnitude of the vector \(\vec a = \hat i + \hat j + \hat k\) is
  • A
    \(\sqrt 3 \;\)
    Correct
  • B
    1-\(\sqrt 3 \)
  • C
    \(\sqrt 2 \)
  • D
    1+\(\sqrt 3 \)
5
Unit vectors along the axes OX, OY and OZ are denoted by
  • A
    \(\hat{i},~\overset{\ddot{\ }}{\mathop{j}}\,and~\hat{k}\)
  • B
    \(\bar i,\;\hat j\;and\;\hat k\)
  • C
    \(\hat i,\;\hat j\;and\;\hat k\)
    Correct
  • D
    $\hat{i},~\overset{\ddot{\ }}{\mathop{j}}\,and~\hat{k}$
6
If a vector \(\vec r\) is expressed in component form as \(\vec r = x\hat i + y\hat j + z\hat k\) then the magnitude of the vector \(\vec r\) is
  • A
    \(\sqrt {{x^2} + 2{y^2} + {z^2}} \)
  • B
    \(\sqrt {{x^2} + {y^2} + 2{z^2}} \)
  • C
    \(\sqrt {{x^2} + {y^2} + {z^2}} \)
    Correct
  • D
    \(\sqrt {2{x^2} + {y^2} + {z^2}} \)
7
If a vector \(\vec r\) is expressed in component form as \(\vec r = x\hat i + y\hat j + z\hat k\) then x, y and z are referred to as
  • A
    scaling factors
  • B
    vector components or rectangular components
    Correct
  • C
    unit vectors
  • D
    unit scalars
8
Which of the following is a vector?
  • A
    energy
  • B
    charge
  • C
    acceleration
    Correct
  • D
    mass
9
In the figure which are the Equal vectors?
Question 9 figure 1
  • A
    vectors \(\vec b\;and\;\vec d\)
    Correct
  • B
    vectors \(\vec a\;and\;\vec d\)
  • C
    vectors \(\vec b\;and\;\vec c\)
  • D
    vectors \(\vec c\;and\;\vec d\)
10
In the figure which are the collinear vectors?
Question 10 figure 1
  • A
    \(\vec a\;and\;\vec d\)
  • B
    \(\vec a\;and\;\vec c\)
    Correct
  • C
    \(\vec b\)\(and\;\vec c\)
  • D
    \(\vec a\;and\;\vec b\)
11
\(\vec a\;\;and - \vec a\)are
  • A
    none of these
  • B
    collinear
    Correct
  • C
    not equal and not collinear
  • D
    equal
12
If two vectors have their corresponding direction cosines equal then the two vectors
  • A
    are at an angle of \(55^\circ \)
  • B
    are at an angle of \(45^\circ \)
  • C
    are parallel
    Correct
  • D
    are perpendicular
13
In triangle ABC, which of the following is not true?
Question 13 figure 1
  • A
    .\(\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} = 0\)
    Correct
  • B
    \(\overrightarrow {AB} - \overrightarrow {CB} + \overrightarrow {CA} = 0\)
  • C
    \(\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = 0\)
  • D
    \(\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {AC} = 0\)
14
If \(\vec a\;and\;\vec b\)are two collinear vectors, then which of the following are incorrect
  • A
    \(\vec b\)=\(\lambda \vec a\) for some scalar λ
  • B
    \(\vec a = \; \pm \;\vec b\)
  • C
    both the vectors\(\vec a\) and\(\vec b\) have same direction, but different magnitudes.
    Correct
  • D
    the respective components of \(\vec a\;and\;\vec b\) are not proportional
15
Magnitude of the vector \(\vec a = \widehat {2i} - 7\hat j - 3\hat k\) is
  • A
    \(\sqrt {65} \)
  • B
    \(\sqrt {61} \)
  • C
    \(\sqrt {63} \)
  • D
    \(\sqrt {62} \;\)
    Correct