MCQs of Vector Algebra

Showing 51 to 60 out of 111 Questions

51.

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

52.

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

53.

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

54.

If \bar{a} = k \bar{i} + 3 \bar{j} and \bar{b} = 4 \bar{i} + k \bar{j} (k \neq 0) are parallel vectors then k =_____

55.

If (\bar{x} - \bar{a}) . (\bar{x} + \bar{a}) = 12 and \bar{a} is unit vector, then \bar{x} =_____

56.

If for vectors \bar{a}, \bar{b} and \bar{c}, \bar{a} + \bar{b} + \bar{c} = 0 |\bar{a}| = 3, |\bar{b}| = 4, |\bar{c}| = 5, then \bar{a} . \bar{b} + \bar{b} . \bar{c} + \bar{c} . \bar{a} =_____

57.

If adjacent sides of a parallelogram are \hat{i} and \hat{i} + \hat{j}, then its area is_____

58.

Area of a triangle whose vertices are (1, 2, 3), (2, 5, -1), and (-1, 1, 2) is _____Sq. unit.

59.

What is called (3, - 3, 3) for \bar{x} = (1, - 1, 1) ?

60.

If for non - zero vectors \bar{x}, \bar{y} \in R^{3} |\bar{x} \times \bar{y}| = 3, |\bar{x}| = 2, |\bar{y}| = 3, then (\bar{x}^\bar{y}) =_____

Showing 51 to 60 out of 111 Questions