MCQs of Vector Algebra

Showing 71 to 80 out of 111 Questions

71.

(\bar{a} \times \bar{b}) . (\bar{c} \times \bar{d})

= _____ .

(a)	$\|\begin{matrix} \bar{b} . \bar{c} & \bar{b} . \bar{d} \\ \bar{a} . \bar{c} & \bar{a} . \bar{d} \end{matrix}\|$
(b)	$\|\begin{matrix} \bar{a} . \bar{c} & \bar{a} . \bar{d} \\ \bar{b} . \bar{c} & \bar{b} . \bar{d} \end{matrix}\|$
(c)	$\|\begin{matrix} \bar{a} . \bar{d} & \bar{a} . \bar{c} \\ \bar{b} . \bar{d} & \bar{b} . \bar{c} \end{matrix}\|$
(d)	$\|\begin{matrix} \bar{b} . \bar{d} & \bar{b} . \bar{c} \\ \bar{a} . \bar{d} & \bar{a} . \bar{c} \end{matrix}\|$

72.

(\bar{x} - \bar{y}) \times (\bar{x} + \bar{y})

= _____ .

73.

The direction cosines of the vector

\bar{x}

= (3, 0, -4) are _____ .

74.

The directions of the vectors (1, 3, 1) and (2, 6, -2) are _____ .

75.

\bar{x}

= (2, 0) and

\bar{y}

= (3, 0), then

|\bar{x} + \bar{y}|

_____

|\bar{x}| + |\bar{y}|

76.

\bar{x}

= (cosα, sinα),

\bar{y}

= (cosβ, sinβ), then

(\bar{x},^{\land} \bar{y})

= _____ .

77.

\bar{x}

= (1, 1, 1),

\bar{y}

= (1, 1, 0) and

\bar{z}

= (1, 0, 0), then

[\bar{x} \bar{y} \bar{z}]

= _____ .

78.

|\bar{a}|

= 2,

|\bar{b}|

= 4,

|\bar{c}|

= 1 and

\bar{a} + \bar{b} = - \bar{c}

, then

\bar{a} . \bar{b} + \bar{b} . \bar{c} + \bar{c} . \bar{a}

= _____ .

79.

The unit vector of magnitude 17

\sqrt{2}

and in the direction opposite to (0, 1, -1) is _____ .

80.

If \bar{a} \times \bar{b} = \bar{c} and \bar{b} \times \bar{c} = \bar{a}, then

Showing 71 to 80 out of 111 Questions