Assertion -If the vectors a and c are non-collinear- then the lines r -6 a - c - 2 c - a and r - a - c - a -3 c intersect in a point Reason- There exist - and - such that the two values of r become same-

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Distance between Two Parallel Planes

Assertion :If...

Question

Assertion :If the vectors $\to a$ and $\to c$ are non-collinear, then the lines $\to r = 6 \to a - \to c + λ (2 \to c - \to a)$ and $\to r = \to a - \to c + μ (\to a - 3 \to c)$ intersect in a point Reason: There exist $λ$ and $μ$ such that the two values of $\to r$ become same.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$R :$ Since $_{1} (2 λ - 1) \to c + (6 - λ) \to a$ and $r_{2} = - (1 + 3 μ) \to c + (1 + μ) \to a$ are not parallel
Two lines will intersect for some value of $λ$ and $μ$
(since they are not parallel) as only two vectors are involved
$\Rightarrow$ Reason is true
$A :$ for $λ = 15, μ = - 10,$
$r_{1} = 29 \to c - 9 \to a$ and $r_{2} = 29 \to c - 9 \to a$
Hence they intersect and it follows from $R$

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Similar questions

Q. Assertion :If vectors

a

and

c

are non collinear then the lines

r = 6 a - c + λ (2 c - a)

and

r = a - c + μ (a + 3 c)

are coplanar Reason: There exist

λ

and

μ

such that the two values of

r

become same.

Assertion (A) Bond angle in ethers is slightly less than the tetrahedral angle.
Reason (R) There is a repulsion between the two bulky (- R) groups.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) If ABCD is a rhombus whose one & Median of a triangle divides it angle is 60^{\circ} then the ratio of the & into two triangles of equal area. lenghts of its diagonals is \sqrt{3} : 1. \end{matrix}$

The correct answer is :(a) /(b)/(c)/(d).

This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

The correct answer is :(a) /(b) /(c) /(d)

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Assertion :If the vectors →a and →c are non-collinear, then the lines →r=6→a−→c+λ(2→c−→a) and →r=→a−→c+μ(→a−3→c) intersect in a point Reason: There exist λ and μ such that the two values of →r become same.

Assertion :If the vectors $\to a$ and $\to c$ are non-collinear, then the lines $\to r = 6 \to a - \to c + λ (2 \to c - \to a)$ and $\to r = \to a - \to c + μ (\to a - 3 \to c)$ intersect in a point Reason: There exist $λ$ and $μ$ such that the two values of $\to r$ become same.