Question

In vectors 3i - 2j+k and 2i +6] + ck what is the value of C to make it perpendicular to each other​

Answer 1

Given:

$\rm \overrightarrow{A} = 3\hat{i}-2\hat{j} + \hat{k} \\ \\ \rm \overrightarrow{B} = 2\hat{i}+6\hat{j} + c\hat{k} \\ \\ \rm \overrightarrow{A} \perp \overrightarrow{B}$

To Find:

Value of c

Answer:

Dot product of perpendicular vector is equal to zero i.e.

$\bf \overrightarrow{A} . \overrightarrow{B} = 0$

So,

$\rm \implies (3\hat{i}-2\hat{j} + \hat{k} ).(2\hat{i}+6\hat{j} + c\hat{k}) = 0 \\ \\ \rm \implies (3 \times 2) - (2 \times 6) + (1 \times c) = 0 \\ \\ \rm \implies 6 - 12 + c = 0 \\ \\ \rm \implies - 6 + c = 0 \\ \\ \rm \implies c = 6$

$\therefore$ $\boxed{\mathfrak{Value \ of \ c = 6}}$