The lengths of the diagonals of a parallelogram constructed on the vectors p-2a-b- q-a-2b- where a- b- are unit vectors forming an angle of 60- are

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Applications of Dot Product

The lengths o...

Question

The lengths of the diagonals of a parallelogram constructed on the vectors $\to p = 2 \to a + \to b$ & $\to q = \to a - 2 \to b,$ where $\to a$ & $\to b$ are unit vectors forming an angle of $60^{\circ}$ are

3

4

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\sqrt{7}

\sqrt{13}

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\sqrt{5}

\sqrt{11}

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None

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\to a = \to p + \to 2 q

\to b + \to 2 p + \to q

\to p

\to q

30^{o}

\to a = \to p + 2 \to q

\to b = 2 \to p + \to q

\to p, \to q

60^{0}

\to p

\to q

30^{o}

\to a = \to p + 2 \to q; \to b = 2 \to p + \to q

\to a, \to b, \to c

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}

\to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

\to a

\to b

(\to a + \to b) . (2 \to a + 3 \to b) \times (3 \to a - 2 \to b) = 0

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