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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`.
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`
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.
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
Find the sum of the vectors `veca = hati -2hatj + hatk, vecb = -2hati + 4hatj + 5hatk and vecc = hati + 6hatj - 7hatk`
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.