The value of p for which vectors \hat{i}+2 \hat{j}+3 ...

CBSE Class 12 Math 2026 All Sets Solved Paper

Question : 13 of 20

Marks: +1, -0

The value of p for which vectors

{i}↖{∧}+2 {j}↖{∧}+3 {k}↖{∧}

and

2 {i}↖{∧}-p {j}↖{∧}+{k}↖{∧}

are perpendicular to each other is

Solution:

Let

{a}↖{→}={i}↖{∧}+2 {j}↖{∧}+3 {k}↖{∧}

{b}↖{→}=2 {i}↖{∧}-p {j}↖{∧}+{k}↖{∧}

{a}↖{→} ⟂ {b}↖{→}

∴ {a}↖{→} ⋅ {b}↖{→}=0

⇒({i}↖{∧}+2 {j}↖{∧}+3 {k}↖{∧}) ⋅(2 {i}↖{∧}-p {j}↖{∧}+{k}↖{∧})=0

⇒(1)(2)+(2)(-p)+(3)(1)=0

⇒ 2-2 p+3=0

⇒ 2 p=5

⇒ p=\;{5}/{2}

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