MCQs of Vector Algebra

Showing 111 to 120 out of 194 Questions

111.

Direction cosines of a vector are l = \frac{3}{5 \sqrt{2}}, m = \frac{4}{5 \sqrt{2}} and n then n =_____

112.

If |\bar{a}| = 2, |\bar{b}| = 3 and \bar{a .} \bar{b} = 0, then \bar{a} x (\bar{a} x (\bar{a} x (\bar{a} x \bar{b}))) =_____

113.

If angle between the vectors 2 x^{2} \hat{i} + 4 x \hat{j} + \hat{k} and 7 \hat{i} - 2 \hat{j} + x \hat{k} is obtuse then =_____

114.

If \bar{a}, \bar{b,} \bar{c} are unit vectors then value of {|\bar{a} - \bar{b}|}^{2} + {|\bar{b} - \bar{c}|}^{2} + {|\bar{c} - \bar{a}|}^{2} is not greater than_____

115.

\bar{a} \times [\bar{a} \times (\bar{a} \times \bar{b})]

= _____ .

116.

\bar{a}

and

\bar{b}

are two unit vectors and measure of angle between them is α. If

\bar{a} + \bar{b}

is a unit vectors, then α = _____ .

117.

For any vector

\bar{r} {(\bar{r} . \hat{i})}^{2} + {(\bar{r} . \hat{j})}^{2} + {(\bar{r} . \hat{k})}^{2}

= _____ .

118.

If the vectors

\bar{a}

\bar{b}

and

\bar{c}

with same magnitude are mutually perpendicular, then measure of angle made by

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

with any of these vectors is _____ .

119.

\bar{u} = \bar{a} - \bar{b}

\bar{v} = \bar{a} + \bar{b}

and

|\bar{a}| = |\bar{b}| = 2

then

|\bar{u} \times \bar{v}|

= _____ .

120.

|(cosθ cosα, cosθ sinα, sinθ)|

= _____ .

Showing 111 to 120 out of 194 Questions