In triangle ABC (Figure), 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
A ship is sailing towards the north at a speed of 1.25 m/s. The current is taking it towards the east at the rate of 1 m/s and a sailor is climbing a vertical pole on the ship at the rate of 0.5 m/s. Find the velocity of the sailor in space.
A isa vector with direction cosines cosα,cosβandcosγ˙ Assuming the y−z plane as a mirror, the directin cosines of the reflected image of A in the plane are a. cosα,cosβ,cosγ b. cosα,−cosβ,cosγ c. −cosα,cosβ,cosγ d. −cosα,−cosβ,−cosγ
Show, by vector methods, that the angularbisectors of a triangle are concurrent and find an expression for the position vector of the point of concurrency in terms of the position vectors of the vertices.
Check whether the given three vectors are coplanar or non-coplanar. −2i^−2j^+4k^,−2i^+4j^,4i^−2j^−2k^