Question

if the vectors a=3i+j-2k, b=-i+3j+4k , c=4i-2j-6k form the sides of the triangle the the lenght of the median bisecting the vector c is

1)√12 units
2)√6 units
3)2√6 units
4)2√3 units

Answer 1

Answer:

(3) Answers is right

Step-by-step explanation:

hop it help

Answer 2

If the vectors a=3i+j-2k, b=-i+3j+4k , c=4i-2j-6k form the sides of the triangle the the lenght of the median bisecting the vector c is

√6 units

Therefore, Option (2) is correct

Step-by-step explanation:

The sides of the triangle are given by

$\vec a=3\hat i+\hat j-2\hat k$

$\vec b=-\hat i+3\hat j+4\hat k$

$\vec c=4\hat i-2\hat j-6\hat k$

Here,

$\vec b+\vec c=\vec a$

The half of the vector c will be

$\frac{\vec c}{2}=\frac{1}{2}(4\hat i-2\hat j-6\hat k)$

$\implies \frac{\vec c}{2}=2\hat i-\hat j-3\hat k$

if the median vector is $\vec d$

Then

$\vec d+\frac{\vec c}{2}=\vec a$

$\implies \vec d=\vec a-\frac{\vec c}{2}$

$\implies \vec d = (3\hat i+\hat j-2\hat k)-(2\hat i-\hat j-3\hat k)$

$\implies \vec d=\hat i+2\hat j+\hat k$

Therefore,

$|\vec d|=\sqrt{1^2+2^2+1^2}$

$\implies |\vec d|=\sqrt{6}$

Hence, the length of the median bisecting vector c is √6 units

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