AP EAMCET · Maths · Vector Algebra

Let $u$ and $v$ be two vectors. Then, $|u - v| = | |u| - |v| |$ if and only if

A $|u| = |v|$
B $u$ and $v$ have the opposite direction
C $u$ and $v$ have the same direction
D $u$ and $v$ are perpendicular to each other

Verified Solution

Answer & Solution

Correct Answer

(C) $u$ and $v$ have the same direction

Step-by-step Solution

Detailed explanation

Let u and v be two vector ⇒u-v=u-v (Given) ⇒(u-v)2=(u-v)2 ⇒u2+v2-2uv=u2+v2-2uv cosθ ⇒cosθ=1 ⇒θ=0, 2π ⇒ u and v have the same direction.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Let u and v be two vectors. Then, u-v=|u-v| if and only if

Step-by-step Solution

Let $u$ and $v$ be two vectors. Then, $|u - v| = | |u| - |v| |$ if and only if