First slide

Algebra of vectors

Question

$If points \hat{i} + \hat{j}, \hat{i} - \hat{j} and p \hat{i} + q \hat{j} + r \hat{k} are collinear, then$

Easy

A

p=1
B

r=0
C

$q \in R$
D

$q \neq 1$

Solution

Points $A (\hat{i} + \hat{j}), B (\hat{i} - \hat{j}) and C (p \hat{i} + q \hat{j} + r \hat{k})$ are collinear
$Now \vec{A B} = - 2 \hat{j} and \vec{B C} = (p - 1) \hat{i} + (q - 1) \hat{j} + r \hat{k}$
$Vectors \vec{A B} and \vec{B C} must be collinear$
$\Rightarrow p = 1, r = 0 and q \neq 1$

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