Question

If a vector Ã=2i+2j+3k and B= 3i+6j+nk are perpendicular to each other then find the value of n​

Answer 1

Answer:

Well that's quite simple if you know the dot product and cross product concept in vectors.When two vectors are perpendicular to each other then their dot product is always equal to 0. As per the vectors rules for dot product:

1. i.i=1

2. j.j=1

3. k.k=1

4. i.j=0

5. j.k=0

6. i.k=0

So if you remember these rules this question is quite easy to solve.What you have to do is multiply the two given vectors according to the dot products rules.

So we have, A.B=0

(2i+2j+3k).(3i+6k+nk)=0

2i.3i + 2j.0j + 3k.(6+n)k =0

6+3(6+n)=0

6+n=-2

n=-8

Therefore the value of n is -8 for the two vectors A and B to be perpendicular.

Answer 2

Answer:

We have,

ABCD as the cyclic quadrilateral in which the diagonal AC and BD.

intersect each other at point P.

also, given that,

AB=8cm,

CD=5cm

Now,

In ΔDCA and ΔAPB,

We have

∠DCP=∠ABP

∠CDP=∠PAB

Hence, 

ΔDPC∼ΔAPB (by A.A property)

According to the given question,

arΔAPBarΔDPC=(ABDC)2

⇒24arΔDPC=(85)2

⇒24arΔDPC=6425

⇒arΔDPV=6425×24

arΔDPC=9.375cm2