Step 1: Given dataA·B=A×BTo find A BStep 2: CalculationA·B=A×B0ex0ex⇒ ABcosθ =ABsinθ(A·B=ABcosθ and A×B=ABsinθ)0ex0ex⇒cosθ =sinθ0ex0ex⇒θ =45°The angle between ...

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

Relation between Trigonometric Ratios

If A·B=A×B. F...

Question

If $\vec{A} \cdot \vec{B} = \vec{A} \times \vec{B}$ . Find $\vec{A} - \vec{B}$

$A - B$

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

$\sqrt{A^{2} + B^{2} - \sqrt{2 A B}}$

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

$A + B$

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

$\sqrt{A^{2} + B^{2} - \sqrt{2} A B}$

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

Open in App

Solution

The correct option is D
$\sqrt{A^{2} + B^{2} - \sqrt{2} A B}$

Step 1: Given data
$\vec{A} \cdot \vec{B} = \vec{A} \times \vec{B}$
To find $\vec{A} - \vec{B}$
Step 2: Calculation
$\vec{A} \cdot \vec{B} = \vec{A} \times \vec{B} \Rightarrow A B \cos θ = A B \sin θ (\vec{A} \cdot \vec{B} = A B \cos θ a n d \vec{A} \times \vec{B} = A B \sin θ) \Rightarrow \cos θ = \sin θ \Rightarrow θ = 45 °$
The angle between the vectors, $θ = 45 °$
Therefore,
$|\vec{A} - \vec{B}| = \sqrt{A^{2} + B^{2} + 2 A B \cos θ} |\vec{A} - \vec{B}| = \sqrt{A^{2} + B^{2} + 2 A B \cos (45 °)} |\vec{A} - \vec{B}| = \sqrt{A^{2} + B^{2} + 2 A B (\frac{1}{\sqrt{2}})} |\vec{A} - \vec{B}| = \sqrt{A^{2} + B^{2} + \sqrt{2} A B}$
Therefore we get, $|\vec{A} - \vec{B}| = \sqrt{A^{2} + B^{2} + \sqrt{2} A B}$
Hence, option D is correct.

Suggest Corrections

Similar questions

Q. For any three vectors

\to a, \to b

and

\to c

, prove that vectors

\to a - \to b, \to b - \to c

and

\to c - \to a

are coplanar.

Q. If

\to a

and

\to b

are two non zero vectors such that

\to a \times \to b = \to b \times \to a,

then

Q. If

\to a, \to b, \to c, \to d

are non-zero vectors, then

[\to a \times \to b \to a \times \to c \to d]

can be simplified as:

Q. If

\to a = 2^i + 2^j + 3^k,

\to b = -^i + 2^j +^k

and

\to c = 3^i +^j

are such that

\to a + λ \to b

is perpendicular to

\to c

then find the value of

λ

Q. If

\to a, \to b

and

\to c

are three non-coplanar vectors and

\to p, \to q

and

\to r

are vectors defined by

\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]}

and

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

, then the value of

(\to a + \to b) \cdot \to p + (\to b + \to c) \cdot \to q + (\to c + \to a) \cdot \to r =

Join BYJU'S Learning Program

If A→·B→=A→×B→. Find A→-B→

If $\vec{A} \cdot \vec{B} = \vec{A} \times \vec{B}$ . Find $\vec{A} - \vec{B}$