The value of m for which the points with position vectors ...

CBSE Class 12 Math 2026 All Sets Solved Paper

Question : 14 of 20

Marks: +1, -0

The value of m for which the points with position vectors

-{i}↖{∧}-{j}↖{∧}+2 {k}↖{∧}, 2 {i}↖{∧}+m {j}↖{∧}+5 {k}↖{∧}

and

3 {i}↖{∧}+11 {j}↖{∧}+6 {k}↖{∧}

are collinear, is

Solution:

Let the three points be A, B & C
Their position vectors are

{O A}↖{→}=2 {i}↖{∧}+m {j}↖{∧}+5 {k}↖{∧}

{O B}↖{→}=3 {i}↖{∧}+11 {j}↖{∧}+6 {k}↖{∧}

{O C}↖{→}=-{i}↖{∧}-{j}↖{∧}+2 {k}↖{∧}

{A B}↖{→}={O B}↖{→}-{O A}↖{→}=(3-2) {i}↖{∧}+(11-m) {j}↖{∧}+(6-5) {k}↖{∧}

={i}↖{∧}+(11-m) {j}↖{∧}+{k}↖{∧}

{B C}↖{→}={O C}↖{→}-{O B}↖{→}=-4 {i}↖{∧}-12 {j}↖{∧}-4 {k}↖{∧}

Now, \;{1}/{-4}=\;{11-m}/{-12}=\;{1}/{-4}

⇒ \;{11-m}/{-12}=\;{1}/{-4}

⇒ 11-m=3

⇒ m=11-3

⇒ m=8

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