MCQs of Vector Algebra

Showing 91 to 100 out of 194 Questions

91.

\bar{x}

= (2, 3, 3),

\bar{y}

= (-2, -3, k), k ≠ -3, then

|\bar{x} . \bar{y}|

_____

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

92.

The area of the parallelogram whose diagonals are

\hat{i} + \hat{j} + \hat{k}

and

\hat{i} - \hat{j} + \hat{k}

is _____ .

93.

The area of the parallelogram whose adjacent sides are

\hat{i} + \hat{j} + \hat{k}

and

\hat{i} - \hat{j} + \hat{k}

is _____ .

94.

\bar{x} = \hat{i} + 3 \hat{j} - 2 \hat{k}

\bar{y} = 2 \hat{i} + 6 \hat{j} + \hat{k}

and

\bar{z} = 2 \hat{i} + a \hat{j} + b \hat{k}

are coplanar and

|\bar{z}|

= 11, then _____ .

95.

A (4, -2), B (5, 2) and C (1, 4), then m∠A = _____ .

96.

If a vector

\bar{r}

makes angles α, β and γ respectively with X-axis, Y-axis and Z-axis, then cos 2α + cos 2β + cos 2γ = _____ .

97.

\bar{a} + \bar{b} + \bar{c} = \bar{0}

and

|\bar{a}| = 3

|\bar{b}| = 5

|\bar{c}| = 7

, then the measure of the angle between

\bar{a}

and

\bar{b}

is _____ .

98.

\bar{a} and \bar{b} are unit vectors and angle between them is θ . If \bar{a} + \bar{b} is a unit vector then_____

99.

\bar{i} . (\bar{j} \times \bar{k}) + \hat{j} . (\hat{i} \times \hat{k}) + \hat{k} . (\hat{i} \times \hat{j}) =_____

100.

If angle between the vectors \bar{a} and \bar{b} and |\bar{a} . \bar{b}| = |\bar{a} \times \bar{b}|, then θ =_____

Showing 91 to 100 out of 194 Questions