Let u→=2i^+j^ and v→=3 i^-5 j^. Consider three points P, Q and R having the position vectors 52i^-2j^,73i^-j^ and 94i^ respectively. Among these, the points in the line passing through u→ and v→ are

AP EAMCET · Maths · Vector Algebra

Let $\vec{u} = 2 \hat{i} + \hat{j}$ and $\vec{v} = 3 \hat{i} - 5 \hat{j}$ . Consider three points $P, Q$ and $R$ having the position vectors $(\frac{5}{2}) \hat{i} - 2 \hat{j}, (\frac{7}{3}) \hat{i} - \hat{j}$ and $(\frac{9}{4}) \hat{i}$ respectively. Among these, the points in the line passing through $\vec{u}$ and $\vec{v}$ are

A Only $P$ and $Q$
B Only $P$ and $R$
C Only $Q$ and $R$
D All $P, Q & R$

Verified Solution

Answer & Solution

Correct Answer

(A) Only $P$ and $Q$

Step-by-step Solution

Detailed explanation

Given that: u→=2i^+j^ and v→=3 i^-5 j^⇒u(2,1) & v(3,-5) Three points P(52,-2), Q(73,-1) and R(94,0) Line passing through u and v: y-y1=y2-y1x2-x1(x-x1) y-1=-5-13-2(x-2) y-1=-6x+12 6x+y=13 Put…

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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