if `veca = hati +hatj + hatk, vecb = 2hati - hatj + 3hatk and vecc = hati - 2hatj + hatk` find a unit vector parallel to the vector `2veca - vecb + 3vecc`
Let `veca = hati + 4hatj + 2hatk, vecb = 3hati - 2hatj + 7hatk ` and `vecc = 2hati - hatj + 4hatk`. Find a vector `vecd` which is perpendicular to both `veca` and `vecb`, and `vecc.vecd = 15`.
In triangle ABC which of the following is not true:
(A) AB + BC + CA = 0
(B) AB+ BC −AC = 0
(C) AB+ BC −CA = 0
(D) AB−CB+CA = 0
If a and b are two collinear vectors, then which of the following are incorrect:
(A) b = λa, for some scalar λ
(B) a = ±b
(C) the respective components of a and b are not proportional
(D) both the vectors a and b have same direction, but different magnitudes.
girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.
Find the sum of the vectors `veca = hati -2hatj + hatk, vecb = -2hati + 4hatj + 5hatk and vecc = hati + 6hatj - 7hatk`
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
The two adjacent sides of a parallelogram are `2hati - 4hatj + 5hatk` and `hati - 2hatj - 3hatk`.
Find the unit vector parallel to its diagonal. Also, find its area.