Question

show that vector a=3i-2j+k , vector b=i-3j+5k and vector c=2i+j-4k forms a right angled triangle?

Answer 1

Given: Vector a = 3i - 2j + k , b = i - 3j + 5k , c = 2i + j - 4k

To find: Show that these vectors forms a right angled triangle?

Solution:

• Now we have given the vectors :

                 a = 3i - 2j + k , b = i - 3j + 5k , c = 2i + j - 4k

• Now we know that for right angle triangle , we have:

                 a^2 + c^2 = b^2

• So applying this, we get:

                 (3i - 2j + k)^2 + (2i + j - 4k)^2 = (i - 3j + 5k)^2

                 9+4+1 + 4+1+16 = 1+9+25

                 14 + 21 = 35

                 35 = 35

• So, both the sides are equal.

Answer:

       Therefore a, b and c are the sides of the right angled triangle .

Answer 2

Answer:

Step-by-step explanation:

The dot product of two vectors a and c is coming 0.

a.c=(3*2)-(2*1)-(1*4)=0

So,a and c are perpendicular vectors.

Hence,they form a right angled triangle.

Hope you understood