The vectors a-b-a-kb- where k is scalar- are collinear for

Let A=a+b and B=a kb Given A and B are collinear. ⇒A =λB ⇒a +b=λ(a kb) On comparing, we get λ=1 and k= 1 ...

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Standard XII

Mathematics

Dot Product

The vectors a...

Question

The vectors $\to a + \to b, \to a - k \to b,$ where $k$ is scalar, are collinear for

k = 1

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k = - 1

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k = 0

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k = 2

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Solution

The correct option is B $k = - 1$
Let $\to A = \to a + \to b$ and $\to B = \to a - k \to b$
Given $\to A$ and $\to B$ are collinear.
$\Rightarrow \to A = λ \to B$
$\Rightarrow \to a + \to b = λ (\to a - k \to b)$
On comparing, we get
$λ = 1$ and $k = - 1$

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Similar questions

Q. If

\to a

and

\to b

are non-collinear vectors, find the value of x for which the vectors

\to α = (2 x + 1) \to a - \to b

and

\to β = (x - 2) \to a + \to b

are collinear.

Q. Show that the points with position vectors

\to a + \to b, \to a - \to b

and

\to a + k \to b

are collinear for all values of

k

Q. Let

\to α = (λ - 2) \to a + \to b

and

\to β = (4 λ - 2) \to a + 3 \to b

be two given vectors where vectors

\to a

and

\to b

are non-collinear. The value of

λ

for which vectors

\to α

and

\to β

are collinear, is:

Q. Let

\to α = (λ - 2) \to a + b

and

\to β = (4 λ - 2) \to a + 3 \to b

be two given vectors where vectors

\to a

and

\to b

non-collinear. The value of

λ

for which vectors

\to α

and

\to β

are collinear, is :

Q. If

\to a

and

\to b

are non-collinear vectors, the value of

x

for which vectors

\to α = (x - 2) \to a + \to b

and

\to β = (3 + 2 x) \to a - 2 \to b

are collinear.

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Dot Product

Standard XII Mathematics

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The vectors →a+→b,→a−k→b, where k is scalar, are collinear for

The correct option is B k=−1Let →A=→a+→b and →B=→a−k→b Given →A and →B are collinear. ⇒→A=λ→B ⇒→a+→b=λ(→a−k→b) On comparing, we get λ=1 and k=−1

The vectors $\to a + \to b, \to a - k \to b,$ where $k$ is scalar, are collinear for

The correct option is B $k = - 1$
Let $\to A = \to a + \to b$ and $\to B = \to a - k \to b$
Given $\to A$ and $\to B$ are collinear.
$\Rightarrow \to A = λ \to B$
$\Rightarrow \to a + \to b = λ (\to a - k \to b)$
On comparing, we get
$λ = 1$ and $k = - 1$