Question

if two vectors 2i+j+k and i+aj+3k are perpendicular to each other then find the magnitude of a​

Answer 1

SOLUTION

GIVEN

The vectors $2 \hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + a\hat{j} + 3 \hat{k}$ are perpendicular to each other

TO DETERMINE

The value of a

EVALUATION

Here the given vectors are

$2 \hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + a\hat{j} + 3 \hat{k}$

Now the vectors are perpendicular to each other

So their dot product = 0

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

$\implies \: 2 + a + 3 = 0$

$\implies \: a + 5 = 0$

$\implies \: a = - 5$

FINAL ANSWER

Hence the required value of a = - 5

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Answer 2

Answer:

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