Question

if A =3i-2j+4k and B=ai +2j k are perpendicular to each other then the value of 'a' is
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Answer 1

Given:

A=3i-2j+4k and B=ai +2j+k are perpendicular to each other.

To find:

Value of "a" ?

Calculation:

Always remember the fact that : when two vectors are perpendicular to one another, the scalar product (dot product) of the vectors will be zero.

As per question , $\vec{A}\perp\vec{B}$

$\therefore \: \vec{A} \: . \: \vec{B} = 0$

$\implies \: (3 \hat{i} - 2 \hat{j} + 4 \hat{k}) \: . \: (a \hat{i} + 2 \hat{j} + \hat{k})= 0$

$\implies \: (3 \times a) + \{( - 2) \times 2 \} + (4 \times 1)= 0$

$\implies \: 3a + (- 4 )+ 4= 0$

$\implies \: 3a - 4 + 4= 0$

$\implies \: 3a + 0= 0$

$\implies \: 3a = 0$

$\implies \: a = \dfrac{0}{3}$

$\implies \: a = 0$

So, value of "a" is 0 (zero).