A- If a-k- b-4-3-4k- c-k- are linearly dependent and -c-3- then - 1- -1 R- For coplanar vectors every vector can be expressed as linear combination of other-

The correct option is B A, R are correct. R is correct explanation of A d=dâ+μb̂ ( linear #160; dependency) d+4μ =1 .........1 ...

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Standard X

Mathematics

Section Formula

A: If a⃗=î+...

Question

$A$ : If $\to a =^i +^i +^k, \to b = 4^i + 3^i + 4^k$ , $\to c =^i + α^j + β^k$ are linearly dependent and $| \to c | = \sqrt{3}$ , then $α = \pm 1, β = 1$
$R$ : For coplanar vectors every vector can be expressed as linear combination of other.

A, R

are correct.

R

is correct explanation of

A

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A, R

are correct,

R

is not correct explanation of

A

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A

is correct,

R

is false

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A

is false,

R

is correct

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Solution

The correct option is B $A, R$ are correct. $R$ is correct explanation of $A$
$d = d^a + μ^b$ ( linear dependency)
$d + 4 μ = 1$ .........1
$d + 3 μ = α$ .........2
$d + 4 μ = β$ ............3
$β = 1$
$| c | = \sqrt{1 + α^{2} + β^{2}}$
$3 = 1 + α^{2} + 1$
$α \pm 1$
If $α = 1$
$μ = 0 d = 1$
$α = - 1$
$μ = 2$
$μ = 2 d = - 7$
Reason is correct and correct explanation of $A$

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Similar questions

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and

\to c =^i + α^j + β^k

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| \to c | = \sqrt{3}

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Q. If

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

, and

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and

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A: If →a=^i+^i+^k,→b=4^i+3^i+4^k, →c=^i+α^j+β^k are linearly dependent and |→c|=√3, then α=±1, β=1R: For coplanar vectors every vector can be expressed as linear combination of other.

The correct option is B A,R are correct. R is correct explanation of Ad=d^a+μ^b ( linear dependency)d+4μ=1.........1d+3μ=α .........2d+4μ=β............3β=1|c|=√1+α2+β23=1+α2+1α±1If α=1μ=0d=1α=−1μ=2μ=2d=−7Reason is correct and correct explanation of A

$A$ : If $\to a =^i +^i +^k, \to b = 4^i + 3^i + 4^k$ , $\to c =^i + α^j + β^k$ are linearly dependent and $| \to c | = \sqrt{3}$ , then $α = \pm 1, β = 1$
$R$ : For coplanar vectors every vector can be expressed as linear combination of other.