If p & s are not perpendicular to each other and r×p=q×p and r·s=0 then r=

r×p=q×p ⇒r−q=λp ⇒r=q+λp take dot with s¯ r·s=q·s+λp·s ⇒q·s+λp·s=0 ⇒λ=-q·sp·s ⇒r=q+λp ⇒r=q-q·sp·sp

If p & s are not perpendicular to each other and r×p=q×p and r·s=0 then r=

r×p=q×p ⇒r−q=λp ⇒r=q+λp take dot with s¯ r·s=q·s+λp·s ⇒q·s+λp·s=0 ⇒λ=-q·sp·s ⇒r=q+λp ⇒r=q-q·sp·sp

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If $p & s$ are not perpendicular to each other and $r \times p = q \times p$ and $r \cdot s = 0$ then $r =$

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q → + q → . p → p → . s → p →

q → + μ p → f o r a l l s c a l a r s μ

p → + s →

q → − q → . s → p → . s → p →

answer is C.

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Detailed Solution

$r \times p = q \times p \Rightarrow r - q = λ p \Rightarrow r = q + λ p$
$take dot with \bar{s}$
$r \cdot s = q \cdot s + λ p \cdot s \Rightarrow q \cdot s + λ p \cdot s = 0 \Rightarrow λ = - \frac{q \cdot s}{p \cdot s} \Rightarrow r = q + λ p \Rightarrow r = q - \frac{q \cdot s}{p \cdot s} p$