Using vector method, show that the points `A(1,-1,0), B(4,-3,1)` and `C(2,-4,5)` are the vertices of a right -angled triangle.

Using vector method, show that the points `A(1,-1,0), B(4,-3,1)` and `

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1.	Using vector method, show that the points `A(1,-1,0), B(4,-3,1)` and `C(2,-4,5)` are the vertices of a right -angled triangle.
Answer» The position vectors of A,B,C are `(hati - hatj),(4hati - 3hatj + hatk)` and `(2hati - 4hatj + 5hatk)` respectively. Show that `vec(AB) + vec(BC) + vec(CA) = vec0` and `\|vec(AB)\|^(2) + \|vec(BC)\|^(2) = \|vec(CA)\|^(2)`. `:. DeltaABC` is right angled at B.

Show that the points `A(1,-2,-8),B(5,0,-2)a n dC(1,3,7)`are collinear, and find the ratio in which `B`divides `A Cdot`
Find the position vector of the mid point of the vector joining thepoints `P(2,3,4)a n d Q(4,1,-2)dot`
Classify the following measures as scalars and vectors : (i) `40` seconds , (ii) `100 m^(2)`, (iii) `30 gm//cm^(3)` (iv) `60 km//hr` , (v) `56 m//s` towards south
Write the different vectors having same magnitude.
Write down the magnitude of each of the following vectors : (i) `veca = hati + 2hatj + 5hatk` , (ii) `vecb = 5hati - 4hatj - 3hatk` (iii) `vecc = (1/(sqrt(3))hati - (1)/(sqrt(3)) hatj + 1/(sqrt(3))hatk)` , (iv) `vecd = (sqrt(2)hati + sqrt(3)hatj - sqrt(5) hatk)`
Find a vector of magnitude 21 units in the direction of the vector `(2hati - 3hatj + 6hatk)`.
Find a vector of magnitude 8 units in the direction of the vector `(5hati - hatj + 2hatk)`.
Find a vector of magnitude 9 units in the direction of the vector `(-2hati + hatj + 2hatk)`.
Find the direction ratios and the direction cosines of the vector joining the points `A(2,1,-2)` and `B(3,5,-4)`.
Find the direction ratios and direction cosines of the vector `veca = (5hati - 3hatj + 4hatk)`.