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a and b are non-collinear vectors. If c = (x - 2) a + b and d = (2x + 1)a - b are collinear vectors, then the value of x = .......
  • a)
    1/2
  • b)
    1/4
  • c)
    1/5
  • d)
    1/3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
a and b are non-collinear vectors. If c = (x - 2) a + b and d = (2x +...
Given, c = (x - 2)a + b and d = (2x + 1)a - b are collinear
∴ c = λd
⇒ (x - 2) a + b = λ[(2x + 1)a - b]
⇒ (x -2)/(2x + 1) = 1/-1 = λ
⇒ 2x + 1 = -x + 2
⇒ 3x = 1
⇒ x = 1/3
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Most Upvoted Answer
a and b are non-collinear vectors. If c = (x - 2) a + b and d = (2x +...
Given Information:
- Vectors a and b are non-collinear.
- c = (x - 2)a + b
- d = (2x + 1)a - b
- c and d are collinear vectors.

Explanation:

Collinear Vectors:
- Two vectors are collinear if they lie on the same line or are scalar multiples of each other.

Condition for Collinearity:
- Two vectors are collinear if there exists a scalar k such that one vector can be obtained by multiplying the other vector by k.

Given Vectors:
- c = (x - 2)a + b
- d = (2x + 1)a - b

Condition for Collinearity:
- Since c and d are collinear, we can write:
(x - 2)a + b = k((2x + 1)a - b)

Comparison of Coefficients:
- Equating the coefficients of a and b on both sides, we get:
x - 2 = k(2x + 1) (for vector a)
1 = -k (for vector b)

Solving Equations:
- From the second equation, k = -1.
- Substituting k = -1 in the first equation:
x - 2 = -2x - 1
3x = 1
x = 1/3
Therefore, the value of x is 1/3. Hence, option 'D' is the correct answer.
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a and b are non-collinear vectors. If c = (x - 2) a + b and d = (2x + 1)a - b are collinear vectors, then the value of x = .......a)1/2b)1/4c)1/5d)1/3Correct answer is option 'D'. Can you explain this answer?
Question Description
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