Question

if A vector= i cap +2j cap -k cap and B vector = 3i cap +4j cap + nk cap, then find the value of n if they are parallel​

Answer 1

SOLUTION

CORRECT QUESTION

GIVEN

The below vectors are parallel

$\vec{A} = \hat{i} + 2\hat{j} - \hat{k}$

$\vec{B} = 3\hat{i} + 6\hat{j} + n \hat{k}$

TO DETERMINE

The value of n

EVALUATION

Here the given vectors are

$\vec{A} = \hat{i} + 2\hat{j} - \hat{k}$

$\vec{B} = 3\hat{i} + 6\hat{j} + n \hat{k}$

Now it is given that the vectors are parallel

So by the given condition

$\sf \dfrac{1}{3} = \dfrac{2}{6} = \dfrac{ - 1}{n}$

$\sf \implies \: \dfrac{1}{3} = - \dfrac{ 1}{n}$

$\sf \implies \: n = - 3$

FINAL ANSWER

Hence the required value of n = - 3

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Answer 2

Explanation:

Given:

$\vec A=\hat i+2 \hat j-\hat k$ and $\vec B=3\hat i+4 \hat j+n\hat k$

To find:Find the value of n if they are parallel.

Solution:

Tip: Angle between both are zero.

Find cross product of both and equate to zero, because sin 0°=0

$\vec A\times\vec B=|A||B|sin\theta$

$\vec A\times\vec B=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\1&2&-1\\3&4&n\end{array}\right|$

$\hat i(2n+4)-\hat j(n+3)+\hat k(4-6)=0$

Thus,

2n+4=0

2n=-4

n=-2

or

-(n+3)=0

n=-3

Final answer:

Value of n=-2 or n=-3

Remark*: These vectors cannot be parallel,because component of k is not zero in cross product.

Hope it helps you.

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