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Question
The vectors `\veca= 2hati - hatj + hatk, \vecb = hati - 3hatj - 5hatk and \vecc = -3hati + 4hatj +4hatk` represents the sides of ______.
Options
an equilateral triangle
an obtuse-angled triangle
an isosceles triangle
a right-angled triangle
MCQ
Fill in the Blanks
Solution
The vectors `\veca= 2hati - hatj + hatk, \vecb = hati - 3hatj - 5hatk and \vecc = -3hati + 4hatj +4hatk` represents the sides of a right-angled triangle.
Explanation:
Given vectors
`veca = 2hati-hatj+hatk`,
`vecb = hati-3hatj-5hatk`
`vecc = -3hati+4hatj+4hatk`,
when two vectors are perpendicular to each other
`vecA*vecB=0`
So, `veca*vecb= (2hati-hatj+hatk).(hati-3hatj-5hatk)`
= [2 + 3 - 5]
`veca*vecb = 0`
So, a Right angled Triangle are formed.
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