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Applications of Dot Product

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c$ are unit vectors such that $\to a$ is perpendicular to the $\to b$ and $\to c$ and angle between $\to b$ and $\to c$ is $\frac{π}{3}$ , then value of $| \to a +$ $\to b +$ $\to c |$ is

A

4

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B

2

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C

9

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D

3

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Solution

The correct option is C $2$
$\begin{matrix} \to a \cdot \to b = 0 \to a \cdot \to c = 0 {∣ ∣ \to a + \to b + \to c ∣ ∣}^{2} = {| a |}^{2} + {| b |}^{2} + {| c |}^{2} + 2 (\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a) = 3 + 2 \to b \cdot \to c = 3 + 2 \times 1 \times 1 \times \frac{1}{2} = 4 ∣ ∣ \to a + \to b + \to c ∣ ∣ = 2 H e n c e, t h e c o r r e c t o p t i o n i s (B) \end{matrix}$

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Similar questions

\to a, \to b, \to c

are unit vectors such that

\to a + \to b + \to c = \to 0

(\to a, \to b) = \frac{π}{3}

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

\to a, \to b, \to c

are unit vectors such that

\to a \cdot \to b = 0 = \to a \cdot \to c

and the angle between

\to b

\to c

\frac{π}{3}

, then the value of

| \to a \times \to b - \to a \times \to c |

\to a, \to b, \to c

are three unit vectors such that

\to a \cdot \to b = \to a \cdot \to c = 0

and the angle between

\to b

\to c

\frac{π}{3},

then the value of

| \to a \times \to b - \to a \times \to c |

\to a, \to b

\to c

be three vectors such that

| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

and the angle between

\to b

\to c

\frac{π}{3} .

\to a

is perpendicular to vector

\to b \times \to c

| \to a \times (\to b \times \to c) |

\to a, \to b, \to c

be three non-zero vectors such that

\to c

is a unit vectors perpendicular is both

\to a

\to b

. If the angle between

\to a

\to b

\frac{π}{6}

[\to a \to b \to c]^{2} = \frac{1}{4} | \to a |^{2} | \to b |^{2}

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