Advertisements
Advertisements
Question
Show that the points A, B, C with position vectors `2hati- hatj + hatk`, `hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle
Solution
Given
`veca = 2hati - hatj + hatk`
`vecb = hati -3hatj - 5hatk`
`vecc = 3hati - 4hatj - 4hatk`
then
`bar(AB) = vecb - veca`
RELATED QUESTIONS
Find the angle between the vectors `hati-hatj and hatj-hatk`
If `veca and vecb` are perpendicular vectors, `|veca+vecb| = 13 and |veca| = 5` ,find the value of `|vecb|.`
Show that the vectors `2hati - 3hatj + 4hatk` and `-4hati + 6hatj - 8hatk` are collinear.
Evaluate the product `(3veca - 5vecb).(2veca + 7vecb)`.
Find `|vecx|`, if for a unit vector veca , `(vecx - veca).(vecx + veca) = 12`.
If `veca.veca = 0` and `veca . vecb = 0,` then what can be concluded about the vector `vecb`?
If either vector `veca = vec0` or `vecb = vec0`, then `veca.vecb = 0`. But the converse need not be true. Justify your answer with an example.
Show that the vectors `2hati - hatj + hatk, hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` from the vertices of a right angled triangle.
If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement:
\[\vec{a} = - \vec{b} \Rightarrow \left| \vec{a} \right| = \left| \vec{b} \right|\]
If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement:
\[|\vec{a}| = |\vec{b}| \Rightarrow \vec{a} = ± \vec{b} \]
If \[\vec{a,} \vec{b}\] are two vectors, then write the truth value of the following statement:
\[\left| \vec{a} \right| = \left| \vec{b} \right| \Rightarrow \vec{a} = \vec{b}\]
The two vectors \[\hat{j} + \hat{k}\] and \[3 \hat{i} - \hat{j} + 4 \hat{k}\] represents the sides \[\overrightarrow{AB}\] and \[\overrightarrow{AC}\] respectively of a triangle ABC. Find the length of the median through A.
Define unit vector.
