Question

If two vectors 2i+3j-k and - 4i-6j-¥k are parallel to each other, then what will be the value of ¥?


Ans:2

Plz provide me the soln

Answer 1

Consider two vectors:

$a_1 \hat{\imath} + b_1 \hat{\jmath} + c_1\hat{k} \\ \\ a_2 \hat{\imath} + b_2 \hat{\jmath} + c_2\hat{k}$


For these two vectors to be parallel, the ratio of all the components must be same:


$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$


Here, the two vectors are:


$2 \hat{\imath} + 3 \hat{\jmath} -\hat{k} \\ \\ -4\hat{\imath} -6 \hat{\jmath} -z\hat{k}$

So, we have the condition:

$\frac{2}{-4} = \frac{3}{-6} = \frac{-1}{-z} \\ \\ \\ \implies -\frac{1}{2} = \frac{1}{z} \\ \\ \\ \implies \boxed{z=-2}$

So, the answer is -2.


If you need the answer as 2, then you need to take the second vector as:

$-4\hat{\imath} + -6\hat{\jmath} + z\hat{k}$
Then you will get the answer as 2. 


Hope it helps
Purva
Brainly Community

Answer 2

Answer:

answer of this question is 2....