Question

Assertion (A) : The vectors a⃗ = 6î + 2ĵ − 8k̂, b⃗ = 10î − 2ĵ − 6k̂ and c⃗ = 4î − 4ĵ + 2k̂ represent the sides of a right angled triangle. Reason (R) : Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

In △ABC, AB→ = î + ĵ + 2k̂ and AC→ = 3î − ĵ + 4k̂. If D is mid-point of BC, then vector AD→ is equal to :

If a = î + ĵ − 2k̂, b = −î + 2ĵ + 2k̂ and c = −î + 2ĵ − k̂ are three vectors, then find a vector perpendicular to both the vectors (a + b) and (b − c).

An instructor at the astronomical centre shows three among the brightest stars in a particular constellation. Assume that the telescope is located at O(0, 0, 0) and the three stars have their locations at the points D, A and V having position vectors 2î + 3ĵ + 4k̂, 7î + 5ĵ + 8k̂ and –3î + 7ĵ + 11k̂ respectively.