Three vectors A- B- and C- satisfy the relation A-B-0 and A-C-0- The vector A is parallel to -

The correct option is D B⃗×C⃗ A⃗ is perpendicular to B⃗ and A⃗ is perpendicular to C⃗ . Thus A⃗ must lie along the direction o ...

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

Byju's Answer

Standard XII

Physics

Work Done as Dot Product

Three vectors...

Question

Three vectors $\to A, \to B$ and $\to C$ satisfy the relation $\to A \cdot \to B = 0$ and $\to A \cdot \to C = 0$ . The vector $A$ is parallel to :

\to B . \to C

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

\to B

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

\to C

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

\to B \times \to C

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

Open in App

Solution

The correct option is D $\to B \times \to C$
$\to A$ is perpendicular to $\to B$ and $\to A$ is perpendicular to $\to C$ . Thus $\to A$ must lie along the direction of the cross product of $\to B$ and $\to C$ .
Alternatively:
Given,
$\to A . \to B = 0$
$\to A . \to C = 0$
$\Rightarrow \to A . \to B - \to A . \to C = \to A (\to B - \to C) = 0$
$\Rightarrow \to A ⊥ (\to B - \to C)$
$\Rightarrow \to A ∥ (\to B \times \to C)$

Suggest Corrections

Similar questions

Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b$ =0, $(\to b - \to a) . (\to b + \to c)$ = 0 and 2 $| \to b + \to c | = | \to b - \to a |$ .

If = $\to a = μ \to b + 4 \to c$ then $μ$ = ______

___

Q. If for three non-zero vectors

\to a, \to b

and

\to c, \to a \cdot \to b = \to a \cdot \to c

and

\to a \times \to b = \to a \times \to c

, then show that

\to b = \to c

Q. Three vectors

\to a, \to b, \to c

. Satisfy the condition

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

. Evaluate

μ = \to a . \to b + \to b . \to c + \to c . \to a

, if

| \to a | = 1; ∣ ∣ \to b ∣ ∣ = 4; | \to c | = 2

Q. If

\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

and

\to c

\frac{π}{3},

then the value of

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

Q. Three vectors

| \to a |, ∣ ∣ \to b ∣ ∣

and

| \to c |

satisfy the condition

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

.
Evaluate the quantity

λ = \to a . \to b + \to b . \to c + \to c . \to a

, if

| \to a | = 1, ∣ ∣ \to b ∣ ∣ = 4 a n d | \to c | = 2

Join BYJU'S Learning Program

Three vectors →A,→B and →C satisfy the relation →A⋅→B=0 and →A⋅→C=0. The vector A is parallel to :

Three vectors $\to A, \to B$ and $\to C$ satisfy the relation $\to A \cdot \to B = 0$ and $\to A \cdot \to C = 0$ . The vector $A$ is parallel to :