When a vehicle's battery is too weak to start the engine using the conventional starter motor, one can resort to alternative methods of starting the vehicle. In the case of a manual transmission vehicle, an effective method known as "push-starting" can be used.

Step-by-Step Explanation:

• Push-Starting Method: This technique involves manually pushing the vehicle to create momentum. The following steps are typically followed:
  • Ensure the vehicle is on a flat or slightly downhill surface to aid in pushing.
  • Turn the ignition key to the "on" position.
  • Engage the clutch and shift the gear lever into second gear. First gear can be used, but second is generally smoother for a push start.
  • With the clutch depressed, allow a few people to push the car forward until it reaches a suitable speed (roughly 5-10 km/h).
  • Once the vehicle is moving at this speed, quickly release the clutch. This will cause the engine to turn over, potentially starting the car.
  • As soon as the engine starts, press the clutch again to stop the car from stalling.
• The other options provided:
  • Starting the vehicle by ignition switch: This method is not applicable as the battery is weak and cannot provide the necessary power.
  • Starting the vehicle by remote switch: Similar to the ignition switch, this method still relies on the battery for power and will not be effective.
  • Starting the vehicle by starter motor: This is the usual method but requires a functional battery, which we don't have in this scenario.

Hence, the correct answer is: "Starting the vehicle by push-starting". This method is practical for manual vehicles with a weakened battery as it bypasses the need for battery power to start the vehicle.