Vector Algebra: The values of a , for which the points A,B,C with position vectors… | AIEEE 2006

AIEEE 2006 (Offline)Question 1

The values of $a$, for which the points $A,B,C$ with position vectors $2\hat i-\hat j+\hat k$, $\hat i-3\hat j-5\hat k$ and $a\hat i-3\hat j+\hat k$ respectively are the vertices of a right angled triangle with $C=\frac\pi2$ are :

Vector Algebra

$2$ and $1$✓ Correct answer$-2$ and $-1$$-2$ and $1$$2$ and $-1$

Solution

$\overrightarrow{CA}=(2-a,2,0)$, $\overrightarrow{CB}=(1-a,0,-6)$. $\overrightarrow{CA}\cdot\overrightarrow{CB}=(2-a)(1-a)=0\Rightarrow a=1,2$.

Vector Algebra - JEE Mathematics question (AIEEE 2006 (Offline))

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