The vector a - -i - 2j - -k lies in the plane of the vectors b - i - j and c - j - k and bisects the angle between b and c - Then- which one of the following gives possible values of - and - -

The correct option is D α = 1, β = 1 a⃗ =λ( b⃗ +c⃗ #160; ) (∵a⃗ lies in plane of b⃗ and c⃗ and bisects the angle between b ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Family of Planes Passing through the Intersection of Two Planes

The vector ...

Question

The vector $\to a = α ˆ i + 2 ˆ j + β ˆ k$ lies in the plane of the vectors $\to b = ˆ i + ˆ j$ and $\to c = ˆ j + ˆ k$ and bisects the angle between $\to b$ and $\to c .$ Then, which one of the following gives possible values of $α$ and $β ?$

α = 2, β = 2

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

α = 1, β = 2

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

α = 2, β = 1

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

α = 1, β = 1

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

Open in App

Solution

The correct option is D $α = 1, β = 1$
$\to a = λ (\to b + \to c)$
$(∵ \to a$ lies in plane of $\to b$ and $\to c$ and bisects the angle between $\to b$ and $\to c)$
$\Rightarrow α \to i + 2 \to j + β \to k = λ (\frac{\to i + \to j}{\sqrt{2}} + \frac{\to j + \to k}{\sqrt{2}})$
$\Rightarrow α \to i + 2 \to j + β \to k = λ (\frac{\to i + 2 \to j + \to k}{\sqrt{2}})$
$\Rightarrow λ = \sqrt{2} α, λ = \sqrt{2} a n d λ = \sqrt{2} β$
$∴ α = β = 1$

Suggest Corrections

Similar questions

Q. The vector

\to a = α^i + 2^j + β^k

lies in the plane of the vectors

\to b =^i +^j

and

\to c =^j +^k

and

\to a

bisects the angle between

\to b

and

\to c .

Then, which one of the following gives the possible values of

α

and

β

Q. The vector

\to a = α^i + 2^j + β^k

lines in the plane of the vectors

\to b =^i +^j

and

\to c =^j +^k

and bisects the angle between

\to b

and

\to c

. Then which one of the following gives possible values

α

and

β

Q. The vector

\to a = α^i + 2^j + β^k

lies in the plane of the vectors

\to b =^i +^j

and

\to c =^j +^k

and bisects the angle between

\to b

and

\to c

. Then , which one if the following gives possible values of

α

and

β

Q. If

a = i + j + k, b = 4 i + 3 j + 4 k

and

c = i + α j + β k

are linearly dependent vectors and

| c | = \sqrt{3}

, then the values of

α

and

β

are respectively.

\to a = α^i + 2^j + β^k

lies in plane of vactor

\to b =^i +^j

and

\to c =^j +^k

and bisects

<

between

\to b

\to c

possible value of

α

and

β

Join BYJU'S Learning Program

The vector →a=αˆi+2ˆj+βˆk lies in the plane of the vectors →b=ˆi+ˆj and →c=ˆj+ˆk and bisects the angle between →b and →c. Then, which one of the following gives possible values of α and β?

The correct option is D α=1,β=1→a=λ(→b+→c)(∵→a lies in plane of →b and →c and bisects the angle between →b and →c)⇒α→i+2→j+β→k=λ(→i+→j√2+→j+→k√2)⇒α→i+2→j+β→k=λ(→i+2→j+→k√2)⇒λ=√2α,λ=√2andλ=√2β∴α=β=1

The vector $\to a = α ˆ i + 2 ˆ j + β ˆ k$ lies in the plane of the vectors $\to b = ˆ i + ˆ j$ and $\to c = ˆ j + ˆ k$ and bisects the angle between $\to b$ and $\to c .$ Then, which one of the following gives possible values of $α$ and $β ?$