Question

3 Assertion : If the sum of the two unit vectors is also a unit vector, then
magnitude of their difference is root of three.
Reason: To find resultant of two vectors, we use square law.​

Answer 1

Assertion : If the sum of the two unit vectors is also a unit vector, then magnitude of their difference is root of three.

reason : To find resultant of two vectors, we use square law.

solution : let a and b are two unit vectors

resultant, R = a + b , here R is also a unit vector

then, |R| = |a + b|

using resultant of vector formula,

⇒1 = √(|a|² + |b|² + 2|a||b|cosθ)

⇒1 = √(1 + 1 + 2 × 1 × 1 cosθ)

⇒1 = √(2 + 2cosθ)

⇒1 = 2 + 2cosθ

⇒cosθ = -1/2

now magnitude of difference of vector = |a - b|

= √{|a|² + |b|² - 2|a||b|cosθ}

= √{1 + 1 - 2 × -1/2 }

= √3

therefore the assertion is correct.

but the reason is incorrect because we use parallelogram law of vector addition instead of square law.