MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Cross Product of Two Vectors

Let a⃗, b⃗ an...

Question

Let $\to a, \to b$ and $\to c$ be three vectors such that $| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10$ and the angle between $\to b$ and $\to c$ is $\frac{π}{3} .$
If $\to a$ is perpendicular to vector $\to b \times \to c$ , then $| \to a \times (\to b \times \to c) |$ is equal to

Open in App

Solution

$| \to a \times (\to b \times \to c) | = | \to a | | \to b \times \to c | sin θ$ where $θ$ is angle between $\to a and \to b \times \to c$
$θ = \frac{π}{2}$ (given)
$\Rightarrow | \to a \times (\to b \times \to c) | = \sqrt{3} | \to b \times \to c | sin \frac{π}{3}$
$\Rightarrow | \to a \times (\to b \times \to c) | = \sqrt{3} \times 5 \times | \to c | \times \frac{\sqrt{3}}{2}$
$\Rightarrow | \to a \times (\to b \times \to c) | = \frac{15}{2} | \to c |$
Now, $| \to b | | \to c | cos θ = 10$
$\Rightarrow 5 | \to c | \frac{1}{2} = 10$
$\Rightarrow | \to c | = 4$
$\Rightarrow | \to a \times (\to b \times \to c) | = 30$

Suggest Corrections

thumbs-up

11

Similar questions

\to a, \to b

\to c

be three unit vector such that

\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)

\to b

is not parallel to

\to c

. then angle between

\to a

\to b

\to a, \to b, \to c

are unit vectors such that

\to a

is perpendicular to the

\to b

\to c

and angle between

\to b

\to c

\frac{π}{3}

, then value of

| \to a +

\to b +

\to c |

\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

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}

\to a, \to b

\to c

be three unit vectors such that

\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b \times \to c) \cdot

\to b

is not parallel to

\to c .

Then the angle between

\to a

\to b

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Cross Product of Two Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon