Given three unit vector a- b- c - no two of which are collinear and satisfies a - b - c -1-2 b- The angle between a and b is equal to

The correct option is D π/2 The given equality implies that nbsp;( a.c ) b ( a.b ) c= 1 / 2 b⇒( a.c 1 / 2 nbsp;) b=( a.b ) c But since b an ...

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

Byju's Answer

Standard XII

Mathematics

Inequalities of Integrals

Given three u...

Question

Given three unit vector $a, b, c;$ no two of which are collinear and satisfies $a \times (b \times c) = \frac{1}{2} b .$ The angle between $a$ and $b$ is equal to

\frac{π}{3}

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

\frac{π}{4}

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

\frac{π}{2}

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

None of these

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

Open in App

Solution

The correct option is D $\frac{π}{2}$
The given equality implies that
$(a . c) b - (a . b) c = \frac{1}{2} b \Rightarrow (a . c - \frac{1}{2}) b = (a . b) c$
But since $b$ and $c$ are non parallel to the only possibility is
$a . c = \frac{1}{2} a$ and $a . b = 0$
Hence the angle between $a$ and $b$ is $\frac{π}{2}$

Suggest Corrections

Similar questions

Q. Let a and b be two unit vectors. If the vectors c=a+2b and d=5a-4b are perpendicular to each other, then the angle between a and b is

Q. If

a, b, c

are the sides opposite to angles

A, B, C

of a triangle

A B C,

respectively and

∠ A = \frac{π}{3}, b : c = \sqrt{3} + 1 : 2,

then the value of

∠ B - ∠ C

Given $\to A + \to B = \to C$ and the magnitudes of vectors $\to A$ , $\to B$ and $\to C$ are respectively 12, 5 and 13 units. The angle between $\to A$ and $\to B$ is

Let the vectors and be such that and, then is a unit vector, if the angle between and is

(A) (B) (C) (D)

Q. If

\to a, \to b, \to c

are unit vectors ,

\to b

and

\to c

are inclined to

\to a

at an angle of

\frac{π}{6}

and the angle between

\to b

and

\to c

\frac{π}{3}

then

(\to a \times \to b) . (\to a \times \to c) =

Join BYJU'S Learning Program

Given three unit vector a, b, c ; no two of which are collinear and satisfies a×(b×c)=12b. The angle between a and b is equal to

The correct option is D π2The given equality implies that(a.c)b−(a.b)c=12b⇒(a.c−12)b=(a.b)cBut since b and c are non parallel to the only possibility is a.c=12a and a.b=0Hence the angle between a and b is π2

Given three unit vector $a, b, c;$ no two of which are collinear and satisfies $a \times (b \times c) = \frac{1}{2} b .$ The angle between $a$ and $b$ is equal to