Three non-perpendicular vectors have magnitudes of 242, 57, 159 Newtons and respectively have angles of 24, 67 and 69 degrees with respect to the x-axis. Find the magnitude of their resultant.
Show that the vectors a = 3i − j + 4k, b = i − 3j − 2k and c = 4i − 3j + 2k are
linearly independent. Find numbers α, β and γ such that d = 2i + 3j − k can be
expressed in the form d = αa + βb + γc.
In a pparallelogramABCD, P divides AB in the ratio 2 : 5 and Q divides DC in the ratio 3 : 2. If AC and PQ intersect at R, find the ratios AR : RC and PR : RQ.
On Monday, the Mars Rover traveled 330 cm. On Tuesday, traveled 180 cm. If the Rover stopped every 15 cm to recharge, how many more times did it need to recharge on Monday than Tuesday?