Let a-b-c- be three vectors having magnitude 1-1 and 2 respectively- If a-a-c-b-0-then the acute angle between a- and c- is

The correct option is B 30^0 a⃗× (a⃗×c⃗)= b⃗ | a⃗× (a⃗×c⃗) |= | b⃗ | (angle between a⃗ amp; a⃗×c⃗ b⃗ 90^0) | a⃗ | | a⃗×c⃗ ...

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

Byju's Answer

Standard XII

Mathematics

Collinear Vectors

Let a⃗,b⃗,c...

Question

Let $\to a, \to b, \to c$ be three vectors having magnitude $1, 1$ and $2$ respectively. If $\to a \times (\to a \times \to c) + \to b = \to 0$ ,then the acute angle between $\to a$ and $\to c$ is

30^{0}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

60^{0}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

45^{0}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

75^{0}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $30^{0}$
$\to a \times (\to a \times \to c) = - \to b$
$| \to a \times (\to a \times \to c) | = ∣ ∣ - \to b ∣ ∣$ (angle between $\to a$ & $\to a \times \to c \to b 90^{0})$
$| \to a | | \to a \times \to c | sin \frac{π}{2} = 1$
$| \to a \times \to c | = 1$
$| \to a | | \to c | sin θ = 1$
$sin θ = \frac{1}{2}$
$θ = 30$

Suggest Corrections

Similar questions

Q. Let

\to a, \to b, \to c

be three vectors having magnitudes

1, 1

and

2

respectively. If

\to a \times (\to a \times \to c) + \to b = \to 0

, then angle between

\to a

and

\to c

Q. Let

\to a, \to b, \to c

be three vectors having magnitude

1, 1

and

2

respectively. If

\to a \times (\to a \times \to c) + \to b = \to 0

, the acute angle between

\to a

and

\to c

Q. Let

\to a, \to b, \to c

be three units vectors such that

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

and the angles between

\to a, \to c

and

\to a, \to b

α

and

β

respectively, then

Q. Let

\to a, \to b, \to c

be vectors of length

3, 4

and

5

respectively. Let

\to a

be perpendicular to

(\to b + \to c), \to b

(\to c + \to a)

and

\to c

(\to a + \to b)

. Find the length of the vector

\to a + \to b + \to c

Q. Let

\to a, \to b

and

\to c

be non-zero vectors such that

(\to a \times \to b) \times \to c = \frac{1}{3} | \to b | | \to c | \to a

. If

θ

is the acute angle between the vectors

\to b

and

\to c

, then

sin θ

equals?

Join BYJU'S Learning Program

Let →a,→b,→c be three vectors having magnitude 1,1 and 2 respectively. If →a×(→a×→c)+→b=→0,then the acute angle between →a and →c is

The correct option is B 300→a×(→a×→c)=−→b|→a×(→a×→c)|=∣∣−→b∣∣ (angle between →a & →a×→c →b 900)|→a||→a×→c|sinπ2=1|→a×→c|=1|→a||→c|sin θ=1sin θ=12θ=30

Let $\to a, \to b, \to c$ be three vectors having magnitude $1, 1$ and $2$ respectively. If $\to a \times (\to a \times \to c) + \to b = \to 0$ ,then the acute angle between $\to a$ and $\to c$ is