For what value of - vector a- and b- perpendicular to each other where a-2 -k- and b-4 -9 -2 k- -

The correct option is D 4As a and b are perpendicular to each other, thus a . b = 0 ⇒ (λ)(4) + (2)( 9) + (1)(2) = 0 ⇒ 4λ 18 + 2 = 0 ⇒ 4λ 16 = 0 ⇒ 4λ =16 ⇒λ ...

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

Byju's Answer

Standard XII

Physics

Multiplication with Vectors

For what valu...

Question

For what value of $λ$ vector $\to a$ and $\to b$ perpendicular to each other where $\to a = λ^i + 2^j +^k$ and $\to b = 4^i - 9^j + 2^k$ ?

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

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

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

Open in App

Solution

The correct option is B 4
As $\to a$ and $\to b$ are perpendicular to each other, thus $\to a . \to b = 0$
$\Rightarrow (λ) (4) + (2) (- 9) + (1) (2) = 0$
$\Rightarrow 4 λ - 18 + 2 = 0$
$\Rightarrow 4 λ - 16 = 0$
$\Rightarrow 4 λ = 16$
$\Rightarrow λ = \frac{16}{4}$
$\Rightarrow λ = 4$

Suggest Corrections

Similar questions

Q. Find a unit vector perpendicular to each of the vectors

\to a + \to b

and

\to a - \to b

where

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

and

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

Q. Find a unit vector perpendicular to each of the vector

\to a + \to b

and

\to a - \to b

, where

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

and

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

Q. Find the projection of the vector

\to a = 4^i - 2^j +^k

on the vector

\to b = 3^i + 6^j + 2^k

. Also find component of

\to a

along

\to b

and perpendicular to

\to b

Q. Find a vector

\to x

which is perpendicular to both

\to A

and

\to B

but has magnitude equal to that of

\to B

. Vector

\to A = 3^i - 2^j +^k

and

\to B = 4^i + 3^j - 2^k

Q. Find a unit vector perpendicular to each of the vector

(\to a + \to b)

and

(\to a - \to b)

, where

\to a =^i +^j +^k

and

\to b =^i + 2^j + 3^k .

Join BYJU'S Learning Program

For what value of λ vector →a and →b perpendicular to each other where →a=λ^i+2^j+^k and →b=4^i−9^j+2^k ?

The correct option is B 4As →a and →b are perpendicular to each other, thus →a.→b=0 ⇒(λ)(4)+(2)(−9)+(1)(2)=0 ⇒4λ−18+2=0 ⇒4λ−16=0 ⇒4λ=16 ⇒λ=164 ⇒λ=4

For what value of $λ$ vector $\to a$ and $\to b$ perpendicular to each other where $\to a = λ^i + 2^j +^k$ and $\to b = 4^i - 9^j + 2^k$ ?

The correct option is B 4
As $\to a$ and $\to b$ are perpendicular to each other, thus $\to a . \to b = 0$
$\Rightarrow (λ) (4) + (2) (- 9) + (1) (2) = 0$
$\Rightarrow 4 λ - 18 + 2 = 0$
$\Rightarrow 4 λ - 16 = 0$
$\Rightarrow 4 λ = 16$
$\Rightarrow λ = \frac{16}{4}$
$\Rightarrow λ = 4$