Vectors> The Vector AB= 3i + 4k and AC = 5i – 2j +...

The Vector AB= 3i + 4k and AC = 5i – 2j + 4k are the sides of a triangle ABC. The length of the median through is
(A) 18^½ (B) 72^½ (C) 33^½(D) 288^½

Faiz Anwar , 7 Years ago

Grade 12th pass

2 Answers

Piyush Kumar Behera

Last Activity: 7 Years ago

A little easy way of approach,

Take A as the origin(0,0)

so Vector AB= 3i + 4k and AC = 5i – 2j + 4k will become position vector.

So coordinate of B is (3,0,4) and C is(5,-2,4).

The mid point of BC can be easily found by midpoint formula of two points as D(4,-1,4).

so length of median through A is AD= $\sqrt{(4-0)^2+(-1-0)^2+(4-0)^2}$

= $\sqrt{33}$

So the answer is C.

I have put my best to explain.If you are unable to get please do write I will try to explain again.And please If my answer is correct do approve my answer!!

Approved

Kushagra Madhukar

Last Activity: 5 Years ago

Dear student,

Please find the attached solution to your answer.

This question would become easy to solve if you notice the similarity between parralelogram law of vector addition and the fact that the diagonal represents the resultant vector and also the diagonals bisects each other.

Let us assume the resultant of vector AC and AB is vector AD. As we know diagonals bisect each other. Hence half of the resultant vector AD will be the median for side BC

Hence, Vector AD = (AC + AB)/2 = (5i – 2j + 4k + 3i + 4k)/2

= (8i – 2j + 8k)/2

= 4i – j + 4k

Hence the length of median = |AD| = (4² + 1² + 4²)^½

= 33^½

Hence C) is the correct option.

Hope it helps.

Thanks and regards,

Kushagra