If the vectors a-1343b-c- -a-b-c and a-b-2c are linearly dependent- then - -

For linearly dependent, the determinant of coefficient matrix is zero ⇒|[ 1 amp; 1343 amp; 1; 1 amp; 1 amp; 1; 1 amp; μ a ...

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

Byju's Answer

Standard XII

Physics

Vectors

If the vector...

Question

If the vectors $\to a + 1343 \to b + \to c, - \to a + \to b + \to c$ and $\to a + μ \to b + 2 \to c$ are linearly dependent, then $μ =$

2014

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

2015

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

2016

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

0

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

Open in App

Solution

The correct option is B $2015$
For linearly dependent, the determinant of coefficient matrix is zero
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1343 & 1 - 1 & 1 & 1 1 & μ & 2 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow 1 (2 - μ) - 1343 (- 2 - 1) + 1 (- μ - 1) = 0 \Rightarrow 2 - μ + 1343 \times 3 - μ - 1 = 0 \Rightarrow - 2 μ + 2 - 1 + 4029 = 0 \Rightarrow - 2 μ + 4030 = 0 \Rightarrow 2 μ = 4030 \Rightarrow μ = \frac{4030}{2} = 2015$

Suggest Corrections

Similar questions

Q. If

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

\to b = 4^i + 3^j + 4^k

and

\to c =^i + α^j + β^k

are linearly dependent vectors and

∣ ∣ \to c ∣ ∣ = \sqrt{3}

then

Q. If the vectors

2 \to a - \to b + \to c, \to a + 2 \to b - \to 3 c, 3 \to a + m \to b + 5 \to c

are linearly dependent, then

m =

Q. If a, b, c form a system of linearly independent vectors then show that the system of vectors

a - 2 b + c, 2 a - b + c

and

3 a + b + 2 c

is also linearly independent.

Q. Assertion :If

\to a =^i, \to b =^j

and

\to c =^i +^j

then

\to a

and

\to b

are linearly independent but

\to a, \to b

and

\to c

are linearly dependent. Reason: If

\to a

and

\to b

are linearly dependent and

\to c

is any vector then

\to a, \to b

and

\to c

are linearly dependent.

Nonzero vectors $\to a, \to b, \to c$ satisfy $\to a . \to b = 0, (\to b - \to a) . (\to b + \to c) = 0 a n d 2 | \to b + \to c | = | \to b - \to a |$ . If $\to a = μ \to b + 4 \to c t h e n μ =$ ___

Join BYJU'S Learning Program

Explore more

Vectors

Standard XII Physics

Join BYJU'S Learning Program

If the vectors →a+1343→b+→c, −→a+→b+→c and →a+μ→b+2→c are linearly dependent, then μ=

The correct option is B 2015For linearly dependent, the determinant of coefficient matrix is zero ⇒∣∣ ∣∣113431−1111μ2∣∣ ∣∣=0 ⇒1(2−μ)−1343(−2−1)+1(−μ−1)=0⇒2−μ+1343×3−μ−1=0⇒−2μ+2−1+4029=0⇒−2μ+4030=0⇒2μ=4030⇒μ=40302=2015

If the vectors $\to a + 1343 \to b + \to c, - \to a + \to b + \to c$ and $\to a + μ \to b + 2 \to c$ are linearly dependent, then $μ =$