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CBSE Class 12 Math 2026 All Sets Solved Paper

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Question : 13 of 20
Marks: +1, -0
The value of p for which vectors i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k} and 2i^−pj^+k^2\hat{i}-p\hat{j}+\hat{k} are perpendicular to each other is
Solution:  
Let a⃗=i^+2j^+3k^\vec{a}=\hat{i}+2\hat{j}+3\hat{k}
b⃗=2i^−pj^+k^\vec{b}=2\hat{i}-p\hat{j}+\hat{k}
a⃗⊥b⃗\vec{a}\perp\vec{b}
∴a⃗⋅b⃗=0\therefore \vec{a}\cdot\vec{b}=0
⇒(i^+2j^+3k^)⋅(2i^−pj^+k^)=0\Rightarrow(\hat{i}+2\hat{j}+3\hat{k})\cdot(2\hat{i}-p\hat{j}+\hat{k})=0
⇒(1)(2)+(2)(−p)+(3)(1)=0\Rightarrow(1)(2)+(2)(-p)+(3)(1)=0
⇒2−2p+3=0\Rightarrow 2-2p+3=0
⇒2p=5\Rightarrow 2p=5
⇒p=  52\Rightarrow p=\;\frac{5}{2}
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