The vectors 2 i +3 j -4 k and a i +b j +c k are perpendicular if … - Vidyadip

MCQ

The vectors $2\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{k}}$ and $\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}$ are perpendicular if :

A
$a = 2, b = 3, c = -4$
✓
$a = 4, b = 4, c = 5$
C
$a = 4, b = 4, c = -5$
D
$a = -4, b = 4, c = -5$

✓

Answer

Correct option: B.

$a = 4, b = 4, c = 5$

It is given that vectors $2\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{k}}$ and $\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}+\text{c}\hat{\text{k}}$ are perpendicular.
So, their dot product is zero.
$\Rightarrow2\text{a}+3\text{b}-4\text{c}=0$
$(\text{b})\text{a}=4;\text{b}=4;\text{c}=5$
$\Rightarrow2(4)+3(4)-4(5)=0$
$8+12-20=0$
$0=0,$ which is true.

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