Let a be a real number and -2-2-a-10k- -12-2a-ak- be three vectors- then - and - are

The correct option is B Linearly independent for all a [α̅β̅γ̅]≠ 0 If #160; α̅ β̅ & γ̅ are noncoplaner 1 amp;2 #160; amp;0 ...

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

Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

Let a be a ...

Question

Let $a$ be a real number and $\to α =^i + 2^j, \to β = 2^i + a^j + 10^k$ , $\to γ = 12^i + 2 a^j + a^k$ be three vectors, then $\to α, \to β$ and $\to γ$ are

Linearly dependent for all

a

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

Linearly independent for all

a

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

Linearly dependent for

a < 0

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

Linearly dependent for

a > 0

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

Open in App

Solution

The correct option is B Linearly independent for all $a$
$[¯ α ¯ β ¯ γ] \neq 0$ If $¯ α ¯ β & ¯ γ$ are noncoplaner
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 0 2 & a & 10 12 & 2 a & a \end{matrix} ∣ ∣ ∣ ∣ = a^{2} - 20 a - 2 (2 a - 120)$
$= a^{2} - 24 a + 240$
$a^{2} - 24 a + 240 > 0$ for all value of a so $¯ α, ¯ β & ¯ γ$ are non coplaner for all value of a.

Suggest Corrections

Similar questions

Q. Let

a

be a real number and

\to α =^i + 2^j, \to β = 2^i + a^j + 10^k

and

\to γ = 12^i + 20^j + a^k

be three vectors, then

\to α, \to β

and

\to γ

are

Q. Let

^{'} a^{'}

be a real number and

\to α =^i + 2^j, \to β = 2^i + a^j + 10^k, \to γ = 12^i + 20^j + a^k

, be three vectors, then

\to α, \to β

and

\to γ

are linearly independent for

Q. Let

\to α, \to β, \to γ

be three unit vectors such that

\to α . \to β = \to α . \to γ = 0

and the angle between

\to β

and

\to γ

30^{\circ} .

Then

\to α

Q. If

\to α = 2^i + 3^j -^k, \to β = -^i + 2^j - 4^k, \to γ =^i +^j +^k

then

(\to α \times \to β) . (\to α \times \to γ) =

Q. Let

\to α, \to β, \to γ

be three unit vectors such that

\to α . \to β = \to α . \to γ

and the angle between

\to β

and

\to γ

30^{o}

. Then

\to α

is ?

Join BYJU'S Learning Program

Let a be a real number and →α=^i+2^j,→β=2^i+a^j+10^k,→γ=12^i+2a^j+a^k be three vectors, then →α,→β and →γ are

The correct option is B Linearly independent for all a[¯α¯β¯γ]≠0 If ¯α ¯β & ¯γ are noncoplaner∣∣ ∣∣1202a10122aa∣∣ ∣∣=a2−20a−2(2a−120) =a2−24a+240a2−24a+240>0 for all value of a so ¯α,¯β&¯γ are non coplaner for all value of a.

Let $a$ be a real number and $\to α =^i + 2^j, \to β = 2^i + a^j + 10^k$ , $\to γ = 12^i + 2 a^j + a^k$ be three vectors, then $\to α, \to β$ and $\to γ$ are