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Unit Vectors

Assertion A...

Question

Assertion ( $A$ ): The points with position vectors $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are collinear if $2 ¯ ¯ ¯ a - 7 ¯ ¯ b + 5 ¯ ¯ c = 0$ .
Reason ( $R$ ): The points with position vectors $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are collinear if $l ¯ ¯ ¯ a + m ¯ ¯ b + n ¯ ¯ c = ¯ ¯ ¯ 0$ .

Both

A

and

R

are true and

R

is correct reason of

A

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Both

A

and

R

are true and

R

is not correct reason of

A

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A

is true

R

is false

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A

is false

R

is true

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Solution

The correct option is D $A$ is true $R$ is false
$\to a, \to b, \to c$ are collinear
$\Rightarrow∋ l, m, n$ all zeros such that
$l \to a + m \to b + n \to c = 0$ if $2 \to a - 7 \to b + 5 \to c = 0$
then $\to a, \to b, \to c$ are collinear since $2 - 7 + 5 = 0$

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Similar questions

Q. Assertion (A)
If the points A(8, 1), B(k, −4) and C(2, −5) are collinear, then k = 4.

Reason (R)
Three points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are collinear only when x₁(y₂− y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) = 0.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a 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).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
The equation

2 x^{2} - 4 x + 3 = 0

has no real roots.

Reason (R)
The equation

a x^{2} + b x + c = 0, (a \neq 0)

has no real roots, if

(b^{2} - 4 a c) < 0 .

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a 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).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
The HCF of two number is 9 and their LCM is 2016. If one of the numbers is 54, then the other is 306.
Reason (R)
For any positive integers a and b, we have:

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

(a) Both Assertion (A) and Reason (R) are true and Reason (A) and Reason (R). For selecting the correct answer, use the following code :

(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.

$\begin{matrix} Assertion (A) & Reason (R) \sqrt{3} i s a n i r r a t i o n a l n u m b e r . & T h e s u m o f a r a t i o n a l n u m b e r a n d a n i r r a t i o n a l n u m b e r i s a n i r r a t i o n a l n u m b e r . \end{matrix} The correct answer is: (a)/(b)/(c)/(d).$

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.

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

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

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Assertion (A): The points with position vectors ¯¯¯a,¯¯b,¯¯c are collinear if 2¯¯¯a−7¯¯b+5¯¯c=0.Reason (R): The points with position vectors ¯¯¯a,¯¯b,¯¯c are collinear if l¯¯¯a+m¯¯b+n¯¯c=¯¯¯0.

The correct option is D A is true R is false→a,→b,→c are collinear⇒∋l,m,n all zeros such that l→a+m→b+n→c=0 if 2→a−7→b+5→c=0then →a,→b,→c are collinear since 2−7+5=0

Assertion ( $A$ ): The points with position vectors $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are collinear if $2 ¯ ¯ ¯ a - 7 ¯ ¯ b + 5 ¯ ¯ c = 0$ .
Reason ( $R$ ): The points with position vectors $¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c$ are collinear if $l ¯ ¯ ¯ a + m ¯ ¯ b + n ¯ ¯ c = ¯ ¯ ¯ 0$ .

The correct option is D $A$ is true $R$ is false
$\to a, \to b, \to c$ are collinear
$\Rightarrow∋ l, m, n$ all zeros such that
$l \to a + m \to b + n \to c = 0$ if $2 \to a - 7 \to b + 5 \to c = 0$
then $\to a, \to b, \to c$ are collinear since $2 - 7 + 5 = 0$