MCQs of Vector Algebra

Showing 101 to 110 out of 194 Questions

101.

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 =_____

102.

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

103.

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} =_____

104.

Area of a parallelogram whose diagonals are \bar{a} = 3 \hat{i} + \hat{j} + \hat{k} and \bar{b} = \hat{i} - 3 \hat{j} + 4 \hat{k} is_____

105.

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

106.

\bar{α} = (x + 4 y) \bar{a} + (2 x + y + 1) \bar{b} and \bar{β} = (y - 2 x + 2) \bar{a} + (2 x - 3 y - 1) \bar{b}, where \bar{a} and \bar{b} are non - zero and non - collinear . If 3 \bar{α} = 2 \bar{β} then_____

107.

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

108.

Volume of a parallelopiped whose adjacent edges are - 12 \hat{i} + α \bar{k}, 3 \bar{j} - \bar{k}, 2 \bar{i} + \bar{j} - 15 \bar{k} is 546 then α =_____

109.

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

110.

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 101 to 110 out of 194 Questions