If a- - - - - - k-b- - 2- - 4k-c- - - - - - 3k- are co-planar then - is-

The correct option is A 5/3 Given vector are ca planer [ [ [ a⃗ #160; amp; b⃗ #160; amp; c⃗ ...

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Byju's Answer

Standard XII

Mathematics

Family of Planes Passing through the Intersection of Two Planes

If a⃗ = î +...

Question

If $\to a =^i +^j +^k, \to b = 2^i - 4^k, \to c =^i + λ^j + 3^k$ are co-planar then $λ$ is?

5 / 3

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Solution

The correct option is A $5 / 3$
Given vector are ca-planer
$\begin{matrix} [\begin{matrix} \to a & \to b & \to c \end{matrix}] = 0 = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 2 & 0 & - 4 1 & λ & 3 \end{matrix} ∣ ∣ ∣ ∣ (0 + 4 λ) - 1 (6 + 4) + 1 (2 λ) = 0 4 λ - 10 + 2 λ = 0 λ = \frac{10}{6} λ = \frac{5}{3} \end{matrix}$
$(A)$ is the correct answer

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Similar questions

Q. If

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

\to c = -^i +^j - 4^k

and

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

, then

| (\to a \times \to b) \times (\to c \times \to d) |

Q. If

\to a = 2^i + 3^j - 4^k, \to b =^i +^j +^k

and

\to c = 4^i + 3^k

, then

| \to a \times (\to b \times \to c) | =

Find the value of $λ$ which will make the vectors $\to a, \to b and \to c$ coplanar, where $\to a = 2^i -^j +^k, \to b =^i + 2^j - 3^k and \to c = 3^i - λ^j + 5^k$ .

Q. I: If

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

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

then

\to a + \to b + \to c = 4^i - 4^j

II: If

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

, then magnitude of

\to a + 2 \to b - 3 \to c

\sqrt{78}

Q. Find the altitude of a parallelopiped determined by

\to a, \to b, \to c

if yhe base

\to a, & \to b

and if

\to a =^i +^j +^k; \to b = 2^i + 4^j -^k & \to c =^i +^j + 3^k

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If →a=^i+^j+^k,→b=2^i−4^k,→c=^i+λ^j+3^k are co-planar then λ is?

The correct option is A 5/3Given vector are ca-planer[→a→b→c]=0=∣∣ ∣∣11120−41λ3∣∣ ∣∣(0+4λ)−1(6+4)+1(2λ)=04λ−10+2λ=0λ=106λ=53(A) is the correct answer

If $\to a =^i +^j +^k, \to b = 2^i - 4^k, \to c =^i + λ^j + 3^k$ are co-planar then $λ$ is?