If r-3-2-5k-a-2-k- b-3-2k- c-2-3k- such that r-a-b-vc- then - -2 - v are in

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

Addition of Vectors

If r⃗=3î+2ĵ...

Question

If $\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k$ , $\to b =^i + 3^j - 2^k, \to c = - 2^i +^j - 3^k$ such that $\to r = λ \to a + μ \to b + v \to c$ , then $μ, \frac{λ}{2}$ , $v$ are in

H . P

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

G . P

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

A . G . P

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

A . P

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

Open in App

Solution

The correct option is D $A . P$
$(3, 2, - 5) = λ (2, - 1, 1) + μ (1, 3, - 2) + γ (- 2, 1, - 3)$
$3 = 2 λ + μ - 2 γ$
$2 = - λ + 3 μ + γ$
$- 5 = λ - 2 μ - 3 γ$
$⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & - 2 - 1 & 3 & 1 1 & 2 & - 3 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} λ μ ν \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 32 - 5 \end{matrix} ⎤ ⎥ ⎦$
$R_{2} \to R_{2} + R_{3}$
$⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & - 2 0 & 1 & - 2 1 & - 2 & - 3 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} λ μ ν \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 3 - 3 - 5 \end{matrix} ⎤ ⎥ ⎦$
$R_{1} \to R_{1} - R_{2}$
$⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 0 0 & 1 & - 2 1 & - 2 & - 3 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} λ μ ν \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 6 - 3 - 5 \end{matrix} ⎤ ⎥ ⎦$
$λ = 3 γ = 2 μ = 1$

Suggest Corrections

Similar questions

Q. If

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

and

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

such that

\to r = l \to a + m \to b + n \to c

, then

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

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. If

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

and

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

. Find

\to a \cdot (\to b \times \to c)

Q. Find

\to a \cdot (\to b \times \to c)

, if

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

and

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

Join BYJU'S Learning Program

If →r=3^i+2^j−5^k,→a=2^i−^j+^k, →b=^i+3^j−2^k, →c=−2^i+^j−3^k such that →r=λ→a+μ→b+v→c, then μ, λ2 , v are in

If $\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k$ , $\to b =^i + 3^j - 2^k, \to c = - 2^i +^j - 3^k$ such that $\to r = λ \to a + μ \to b + v \to c$ , then $μ, \frac{λ}{2}$ , $v$ are in