If the vectors a -2 -k- b - I -2 -3 k- and c -3 -5 k- are coplanar- then value of - is

A⃗ = 2î ĵ+k̂ b⃗ = î+2 ĵ 3 k̂ c⃗ = 3 î λĵ+5 k̂ For vectors to be coplanar, a⃗.(b⃗×c⃗)=0 2 amp; 1 amp; 1 1 amp; 2 amp; 3 3 amp; λ amp; ...

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

Byju's Answer

Standard XII

Mathematics

Applications Scalar Triple Product

If the vector...

Question

If the vectors $\to a = 2^i -^j +^k$ , $\to b = I + 2^j - 3^k$ and $\to c = 3^i - λ^j + 5^k$ are coplanar, then value of $λ$ is

Open in App

Solution

$\to a = 2^i -^j +^k \to b =^i + 2^j - 3^k \to c = 3^i - λ^j + 5^k$

For vectors to be coplanar,

$\to a . (\to b \times \to c) = 0$

$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & 1 1 & 2 & - 3 3 & - λ & 5 \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow 2 (10 - 3 λ) + 1 (5 + 9) + 1 (- λ - 6) = 0 \Rightarrow 20 - 6 λ + 14 - λ - 6 = 0 \Rightarrow 7 λ = 28 ∴ λ = 4$ .

Suggest Corrections

Similar questions

Q. If the vectors

2^i -^j +^k,^i + 2^j - 3^k

and

3^i + λ^j + 5^k

be coplanar, then

λ =

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. If vectors

2^i -^j +^k,^i + 2^j - 3^k

and

3^i + a^j + 5^k

are coplanar, then find the value of

a

Q. Find the value of

\to a

if the vectors

2^i -^j +^k,^i + 2^j - 3^k

and

3^i + a^j + 5^k

are coplanar?

Q. The value of x such that the vectors

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

and

c = 3^i - 4^j + 5^k

are coplanar is

Join BYJU'S Learning Program

If the vectors →a=2^i−^j+^k, →b=I+2^j−3^k and →c=3^i−λ^j+5^k are coplanar, then value of λ is

→a=2^i−^j+^k→b=^i+2^j−3^k→c=3^i−λ^j+5^k For vectors to be coplanar, →a.(→b×→c)=0 ∣∣ ∣∣2−1112−33−λ5∣∣ ∣∣=0 ⇒2(10−3λ)+1(5+9)+1(−λ−6)=0⇒20−6λ+14−λ−6=0⇒7λ=28∴λ=4.

If the vectors $\to a = 2^i -^j +^k$ , $\to b = I + 2^j - 3^k$ and $\to c = 3^i - λ^j + 5^k$ are coplanar, then value of $λ$ is