Three vectors P are shown in the figure- Let S be any point on the vector R-T he distance between the point P and S is b- R- The general relation among vectors P-Q and S is

The correct option is A S = ( 1 b)P + bQ As given distance between P and S =b|R Therefore S P=b|R| S P=b(Q P)[R=Q P] S P=bQ bP S=P+bQ ...

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Byju's Answer

Standard XII

Physics

Vector Component

Three vectors...

Question

Three vectors $\to P$ are shown in the figure. Let S be any point on the vector $\to R$ .T he distance between the point P and S is $b ∣ ∣ ∣ \to R ∣ ∣ ∣$ . The general relation among vectors $\to P, - \to Q a n d \to S$ is

\to S = (1 - b) \to P + b - \to Q

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\to S = (1 - b^{2}) \to P + b - \to Q

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\to S = (b - 1) \to P + b - \to Q

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\to S = (1 - b) \to P + b^{2} - \to Q

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Solution

The correct option is A $\to S = (1 - b) \to P + b - \to Q$
As given distance between P and S $= b | \to R$
Therefore
$\to S - \to P = b | \to R | \to S - \to P = b (- --- \to Q - \to P) [\to R = \to Q - \to P] \to S - \to P = b \to Q - b \to P \to S = \to P + b \to Q - b \to Q \to S = \to P - b \to P + b \to Q \to S = \to P (1 - \to b) + b \to Q$
$∴$ General relation $\Rightarrow \to P (1 - \to b) + b \to Q$

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